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25 March 2026, Volume 46 Issue 2 Previous Issue   

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DOMAIN VARIATIONS AND POHOZAEV IDENTITIES FOR WEAK SOLUTIONS OF $p$-LAPLACIAN EQUATION Shusen YAN, Huansong ZHOU Acta mathematica scientia,Series B. 2026, 46 (2):  519-528.  DOI: 10.1007/s10473-026-0201-7 Abstract ( 52 )   Save Using the domain variation estimate, we give a new proof of the local Pohozaev identities for weak solutions of elliptic equations involving $p$-Laplacian operators under only $C^1$-regularity of the solutions. As an application, we obtain the Pohozaev identities for $C^1$ solution of $p$-Laplacian equation in $\mathbb{R}^N$ with $1<p<N$. References | Related Articles | Metrics

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EXISTENCE AND MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE PLANAR SCHRODINGER-POISSON SYSTEM WITH EXPONENTIAL CRITICAL GROWTH Xueqin PENG Acta mathematica scientia,Series B. 2026, 46 (2):  529-548.  DOI: 10.1007/s10473-026-0202-6 Abstract ( 21 )   Save The paper deals with the following planar Schrödinger-Poisson system $\begin{equation*} \begin{cases}-\Delta u+\lambda u+\phi u= f(u),&\text{in}~\mathbb{R}^{2},\\-\Delta\phi= u^2,&\text{in}~\mathbb{R}^{2},\\ \int_{\mathbb{R}^{2}}u^2{\rm d}x=a^2,~u\in H^1(\mathbb{R}^2), \end{cases} \end{equation*}$ where $a\in(0,1)$, $\lambda \in \mathbb{R}$ is an undetermined parameter which appears as a Lagrange multiplier and $f$ satisfies the exponential critical growth. Under suitable conditions on $f$, we manage to establish such critical points which emerge as a local minimizer or correspond to a mountain pass. Furthermore, by using genus theory, we obtain infinitely many solutions. The proofs are based upon the reduction method by working on a natural constraint, which is introduced by Bartsch and Soave [J Funct Anal, 2017, 272: 4998-5037]. Our results complement the results made by Cingolani and Jeanjean [SIAM J Math Anal, 2019, 51: 3533-3568] where handle the Sobolev subcritical case. References | Related Articles | Metrics

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EXISTENCE AND STABILITY ANALYSIS OF EVOLUTIONARY DIFFERENTIAL HEMIVARIATIONAL INEQUALITIES IN BANACH SPACES Wei LI, Ke XU, Rong HU, Zhiyang MA Acta mathematica scientia,Series B. 2026, 46 (2):  549-567.  DOI: 10.1007/s10473-026-0203-5 Abstract ( 137 )   PDF (442KB) ( 74 )   Save In this paper, we introduce and study a new class of evolutionary differential hemivariational inequalities in Banach spaces. Using a fixed-point theorem, we first establish the existence and uniqueness of mild solutions for the evolutionary differential hemivariational inequality. Building on this result, we then investigate the stability of the evolutionary differential hemivariational inequality problem under perturbations of the mappings, constraint set, and infinitesimal generator of the $C_0$-semigroup ${\rm e}^{tB}$. References | Related Articles | Metrics

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GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR INITIAL-BOUNDARY VALUE PROBLEMS OF ONE-DIMENSION QUASILINEAR WAVE EQUATIONS WITH NULL CONDITIONS Dongbing ZHA, Yitong SUN, Tingqiang HOU Acta mathematica scientia,Series B. 2026, 46 (2):  568-594.  DOI: 10.1007/s10473-026-0204-4 Abstract ( 12 )   Save We consider the initial-boundary value problems on $\mathbb{R}^{+}\times \mathbb{R}^{+}$ for one-dimension systems of quasilinear wave equations with null conditions. We first show that for homogeneous Dirichlet boundary values and sufficiently small initial data, classical solutions always globally exist. Then we prove that the global solution will scatter, i.e., it will converge to some solution of one dimensional homogeneous linear wave equations as time tends to infinity, in the energy sense. Finally we show the inverse scattering result: the scattering data can determine the global solution uniquely. References | Related Articles | Metrics

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FORMATION OF SINGULARITIES FOR AW-RASCLE TRAFFIC MODEL WITH RELAXATION Min DING, Xiaohui LI, Jianlin XIANG Acta mathematica scientia,Series B. 2026, 46 (2):  595-604.  DOI: 10.1007/s10473-026-0205-3 Abstract ( 11 )   Save We study the singularity formation of smooth solutions for Cauchy problem of the Aw-Rascle traffic model with relaxation. Under the subcharacteristic assumption and general law of the velocity deviation, we construct a set of large initial data, and prove that the corresponding smooth solutions blow up in a finite time, and form a cusp singularity in the direction of genuinely nonlinear characteristic. Moreover, under the generic nondegenerate condition on initial data, we give precise description on the blowup time and location. References | Related Articles | Metrics

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VORTEX PATCHES FOR THE EULER EQUATIONS IN A FINITE CHANNEL Xinyao WANG, Xiaohuan WANG Acta mathematica scientia,Series B. 2026, 46 (2):  605-616.  DOI: 10.1007/s10473-026-0206-2 Abstract ( 9 )   Save By making use of an adaption of Arnold variational principle [4], we construct a family of vortex patches of the inviscid, incompressible steady flow in a finite channel $\mathbb{T} \times [0,1]$. References | Related Articles | Metrics

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WELL-POSEDNESS AND BLOW-UP CRITERION FOR A CHERN-SIMONS GAUGED NONLINEAR SCHRÖDINGER EQUATION Qianqian BAI, Yongsheng JIANG, Xiaoguang LI, Jun WANG Acta mathematica scientia,Series B. 2026, 46 (2):  617-641.  DOI: 10.1007/s10473-026-0207-1 Abstract ( 15 )   Save This paper investigates the Cauchy problem for the Chern-Simons gauged nonlinear Schrödinger equation with a power-type nonlinearity. Previous studies on this equation usually relied on restrictive assumptions, such as radial symmetric initial data or mass-critical exponent ($p=4$). This work overcomes these limitations by employing Kato's theorem, energy method, and an approximation technique. Specifically, for both cases of mass-critical exponent and mass-supercritical exponent ($p>4$), we establish the local well-posedness of the Cauchy problem without the assumption of radial symmetry property to the initial data. Additionally, a sharp threshold is obtained for the global existence and blow-up to time-dependent solutions. References | Related Articles | Metrics

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CONCENTRATION PHENOMENA AND COMPETITION EFFECTS FOR FRACTIONAL KIRCHHOFF-CHOQUARD EQUATIONS WITH EXPONENTIAL GROWTH Tahir BOUDJERIOU, Vicenţiu D. RĂDULESCU, Thin Van NGUYEN Acta mathematica scientia,Series B. 2026, 46 (2):  642-696.  DOI: 10.1007/s10473-026-0208-0 Abstract ( 11 )   Save In this paper, we study the fractional Kirchhoff-Choquard equation $\begin{align*} &M\bigg([u]_{s,p}^{p}+\varepsilon^{-N}\int\limits_{\mathbb R^N}V( x)|u|^{p}{\rm d}x\bigg)(\varepsilon^{N}(-\Delta)_{p}^{s}u+V(x)|u|^{p-2}u)\\ =\,&\varepsilon^{\mu-N}\bigg(\int\limits_{\mathbb R^N}\dfrac{Q(y)F(u(y))}{|x-y|^{\mu}}{\rm d}y\bigg)Q(x)f(u(x))\quad\text{in}\; \mathbb R^{N}, \end{align*}$ where $\varepsilon$ is a positive parameter, $N=ps, p\ge 2, s\in (0,1),0<\mu<N.$ The Kirchhoff function $M(t)=a+bt, a>0,b>0$, nonlinear function $f$ has the exponential growth, potential functions $V$ and $Q$ are continuous functions satisfying some suitable conditions. Using Ljusternik-Schnirelmann category theory and variational methods, we establish the multiplicity and concentration of positive solutions for small values of the parameter. References | Related Articles | Metrics

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THE LP DUAL MINKOWSKI TYPE PROBLEM FOR MIXED HESSIAN QUOTIENT TYPE EQUATIONS WITH $p\geq q$ Ni Xiang, Yuni Xiong Acta mathematica scientia,Series B. 2026, 46 (2):  697-713.  DOI: 10.1007/s10473-026-0209-z Abstract ( 9 )   Save In this paper, we establish the {\it a priori} estimates for solutions of mixed Hessian quotient type equations on $\mathbb{S}^n$. Then we obtain the existence and uniqueness of $\widetilde{\Gamma}_k$-admissible solutions to the $L_p$ dual Minkowski type problem with $p\geq q$. Moreover, we show the existence of convex solutions by Constant Rank Theorem. References | Related Articles | Metrics

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UNIVERSAL INEQUALITIES FOR EIGENVALUES OF THE DIRICHLET LAPLACIAN ON CONFORMALLY FLAT RIEMANNIAN MANIFOLDS Yong LUO, Xianjing ZHENG Acta mathematica scientia,Series B. 2026, 46 (2):  714-729.  DOI: 10.1007/s10473-026-0210-6 Abstract ( 7 )   Save In this paper we study eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds. In particular we establish some universal inequality for eigenvalues of the Dirichlet Laplacian on the hyperbolic space $\mathbb{H}^n(-1)$. References | Related Articles | Metrics

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ON CONVERGENCE PROPERTIES FOR GENERALIZED SCHR ÖDINGER OPERATORS ALONG TANGENTIAL CURVES Huiju WANG, Wenjuan LI Acta mathematica scientia,Series B. 2026, 46 (2):  730-751.  DOI: 10.1007/s10473-026-0211-5 Abstract ( 9 )   Save In this paper, we consider convergence properties for generalized Schrödinger operators along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$ with less smoothness comparing with Lipschitz condition. Firstly, we obtain sharp convergence rate for generalized Schrödinger operators with polynomial growth along tangential curves in $\mathbb{R}^{n} \times \mathbb{R}$, $n \ge 1$. Secondly, we get the convergence result along a family of restricted tangential curves in $\mathbb{R} \times \mathbb{R}$. As a corollary, we obtain the sharp $L^p$-Schrödinger maximal estimates along tangential curves in $\mathbb{R} \times \mathbb{R}$. References | Related Articles | Metrics

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PARABOLIC FREQUENCY MONOTONICITY FOR TWO NONLINEAR EQUATIONS UNDER RICCI FLOW Chuanhuan LI, Yi LI, Kairui XU, Jichun ZHU Acta mathematica scientia,Series B. 2026, 46 (2):  752-766.  DOI: 10.1007/s10473-026-0212-4 Abstract ( 13 )   Save In this paper, we study the parabolic frequency for positive solutions of two nonlinear parabolic equations under the Ricci flow on closed manifolds. The first equation is $\partial_{t}u=\Delta_{g(t)}u+au+|\nabla_{g(t)} u|^{2}$ with a constant $a$; the other one is $\partial_{t}u=\Delta_{g(t)} u+\lambda u^{p}$ with two constants $\lambda$ and $p\geq1$. Here $g(t)$ is the Riemannian metric involved by Ricci flow. We establish the monotonicity of the parabolic frequency for the solutions of two nonlinear parabolic equations with bounded Ricci curvature. Subsequently, we apply the parabolic frequency monotonicity to derive some integral type Harnack inequalities. Additionally, we use $-K_{1}$ instead of the lower bound $0$ of Ricci curvature from Theorem 1.3 in \cite{LLX-2023}, where $K_{1}$ is any positive constant. References | Related Articles | Metrics

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OPTIMAL MULTIPOLAR HARDY INEQUALITIES ON THE HEISENBERG GROUP Yongyang JIN, Li TANG, Zhoutao HU, Tianqi LOU Acta mathematica scientia,Series B. 2026, 46 (2):  767-780.  DOI: 10.1007/s10473-026-0213-3 Abstract ( 6 )   Save Based on the left-invariant property of the standard vector fields, we prove a class of one-parameter multipolar Hardy inequalities on the Heisenberg group by the method of super-solutions. Furthermore, we obtain the criticality of the corresponding Schrödinger operators in certain parameter range by constructing suitable sequence of minimization functions, which means that we have got some optimal multipolar Hardy inequalities on the Heisenberg group. The attainability of the sharp constant is also considered, unlike the case of unipolar classical Hardy inequality, the sharp constant is attained for certain parameter range in the multipolar case. References | Related Articles | Metrics

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SHARP INEQUALITIES FOR LOGARITHMICALLY SUBHARMONIC FUNCTIONS ON $\mathbb{R}^n$ Jineng DAI Acta mathematica scientia,Series B. 2026, 46 (2):  781-789.  DOI: 10.1007/s10473-026-0214-2 Abstract ( 14 )   Save In this paper we obtain some sharp inequalities for logarithmically subharmonic functions on $\mathbb{R}^n$, which extends and simplifies some previously known results. References | Related Articles | Metrics

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THE BOHR'S PHENOMENON FOR THE CLASS OF K-QUASICONFORMAL HARMONIC MAPPINGS Raju BISWAS, Rajib MANDAL Acta mathematica scientia,Series B. 2026, 46 (2):  790-811.  DOI: 10.1007/s10473-026-0215-1 Abstract ( 11 )   Save The primary objective of this paper is to establish several sharp versions of improved Bohr inequality, refined Bohr-type inequality, and refined Bohr-Rogosinski inequality for the class of $K$-quasiconformal sense-preserving harmonic mappings $f=h+\bar{g}$ in the unit disk $\mathbb{D}: = \{z\in\mathbb{C}: |z| < 1\}$. In order to achieve these objectives, we employ the non-negative quantity $S_\rho(h)$ and the concept of replacing the initial coefficients of the majorant series by the absolute values of the analytic function and its derivative, as well as other various settings. Moreover, we obtain the sharp Bohr-Rogosinski radius for harmonic mappings in the unit disk by replacing the bounding condition on the analytic function $h$ with the half-plane condition. References | Related Articles | Metrics

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BOUNDEDNESS OF THE BERGMAN TYPE OPERATOR $T_{\lambda,\tau,c,k,k'}$ FROM $L^{p}(B_{n}, {\rm d}v_{\alpha})$ TO $L^{q}(B_{n}, {\rm d}v_{\beta})$ Xuejun ZHANG, Min ZHOU Acta mathematica scientia,Series B. 2026, 46 (2):  812-825.  DOI: 10.1007/s10473-026-0216-0 Abstract ( 11 )   Save Bergman type operators are closely related to many basic problems on operator theory and function space theory. In this paper, we characterize the boundedness of logarithmic Bergman type operator $T_{\lambda,\tau,c,k,k'}$ from $L^{p}(B_{n}, {\rm d}v_{\alpha})$ to $L^{q}(B_{n}, {\rm d}v_{\beta})$ for some $1\leq p,q\leq+\infty$ and real $\alpha,\beta$. These results generalize the relevant work of some scholars. At the same time, we partially solve the problem, put forward by Chen et al. in JMAA (2024). References | Related Articles | Metrics

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THE FORMAL GEOMETRY OF A CONTRACTIVE QUANTUM PLANE AND TAYLOR SPECTRUM Anar DOSI Acta mathematica scientia,Series B. 2026, 46 (2):  826-875.  DOI: 10.1007/s10473-026-0217-z Abstract ( 12 )   Save The paper is devoted to noncommutative formal geometry of a contractive quantum plane, whose spectrum is the union of two copies of the complex plane. It turns out that a formal completion of the Arens-Michael envelope of a contractive quantum plane results in a noncommutative analytic space, whose base topological space is the same spectrum, whereas the structure sheaf is obtained as a certain quantization of the related commutative analytic space. As the basic tool we use the fibered products of the Fréchet sheaves. The related topological homology problems are considered to find out a key link between the transversality relation of the noncommutative sections versus to a left Fréchet module, and noncommutative Taylor spectrum of the module. References | Related Articles | Metrics

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LIMITING ABSORPTION PRINCIPLE FOR LONG-RANGE PERTURBATION IN THE DISCRETE TRIANGULAR LATTICE SETTING Nassim ATHMOUNI, Marwa ENNACEUR, Sylvain GOL ÉNIA, Amel JADLAOUI Acta mathematica scientia,Series B. 2026, 46 (2):  876-896.  DOI: 10.1007/s10473-026-0218-y Abstract ( 13 )   Save We examine the discrete Laplacian acting on a triangular lattice, introducing long-range perturbations to both the metric and the potential. Our goal is to establish a Limiting Absorption Principle away from possible embedded eigenvalues. Our study relies on a positive commutator technique. References | Related Articles | Metrics

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THRESHOLD ANALYSIS OF IMPULSIVE CONTROL IN A MOSQUITO POPULATION SUPPRESSION MODEL WITH SPARSE STATE FEEDBACK Shouzong LIU, Yang XU, Mingzhan HUANG Acta mathematica scientia,Series B. 2026, 46 (2):  897-919.  DOI: 10.1007/s10473-025-0219-x Abstract ( 9 )   Save In this study, a mosquito population suppression model that integrates stage structure is introduced, which serves as the foundation for exploring various strategies for the periodic impulsive release of sterile mosquitoes, including those that either incorporate or disregard population state feedback, as well as a composite control approach. We identify release thresholds under different strategies that ensure the complete eradication of the wild mosquito population. Numerical analyses are conducted to evaluate the performance of these release strategies. Our findings reveal that integrating state feedback mechanisms can effectively prevent the blindness of release behaviors. Key factors such as the release interval, frequency of population assessments, and control intensity significantly influence the reduction of the cumulative release quantity of sterile mosquitoes, the shortening of control duration, and the decrease in effective release events. The influence of these factors on control outcomes across different strategies and scenarios is also examined. References | Related Articles | Metrics

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G-BESSEL PROCESSES AND RELATED PROPERTIES Mingshang HU, Renxing LI Acta mathematica scientia,Series B. 2026, 46 (2):  920-936.  DOI: 10.1007/s10473-026-0220-4 Abstract ( 11 )   Save In this paper, we introduce $ G $-Bessel processes for a class of $ d $-dimensional $ G $-Brownian motions. Under the condition of dimensionality $ d $, we obtain that the $ G $-Bessel process is the solution of the stochastic differential equation. Furthermore, under the stricter condition of dimensionality, we establish the existence and uniqueness of a solution of the stochastic differential equation governing the $ G $-Bessel process and prove the nonattainability of the origin for $ G $-Brownian motion. References | Related Articles | Metrics

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DEVIATION PROBABILITIES FOR SPECTRAL RADIUS OF PRODUCTS OF COMPLEX GINIBRE ENSEMBLES Yutao MA, Chaoyang SONG Acta mathematica scientia,Series B. 2026, 46 (2):  937-956.  DOI: 10.1007/s10473-026-0221-3 Abstract ( 8 )   Save Let $\boldsymbol{X}_1, \cdots, \boldsymbol{X}_{m_n}$ be independent $n\times n$ complex Ginibre ensembles and $Z_1, \cdots,$ $ Z_n$ be the eigenvalues of $\prod_{j=1}^{m_n} \boldsymbol{X}_j.$ Suppose $\lim\limits_{n\to\infty}m_n=+\infty,$ we obtain large and moderate deviations for $\max_{1\le i\le n} \log |Z_i|.$ References | Related Articles | Metrics

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ENERGY SCHEDULING IN MULTI-SENSOR ESTIMATION OVER PACKET DROPPING CHANNELS WITH IMPERFECT ACKNOWLEDGMENTS AND ENERGY CONSTRAINTS Zhiping JU, Lijun GUO, Guoliang WEI, Jiajia LI Acta mathematica scientia,Series B. 2026, 46 (2):  957-970.  DOI: 10.1007/s10473-026-0222-2 Abstract ( 8 )   Save In this paper, the optimal energy scheduling problem is investigated in the sensor network with energy sharing and imperfect feedback information. Each sensor is equipped with an energy harvesting module and a transceiver device for the energy sharing between adjacent sensors. Sensors can transmit information and receive packet receipt acknowledgments from the remote estimator via erroneous feedback channels. The goal of this paper is to determine the energies used for data transmission and for sharing between sensors to ensure high-quality estimation performance. To address the challenges posed by imperfect feedback, a novel approach is first proposed for the synergistic estimation of the probability distribution of feedback information for each sensor. Subsequently, a joint error covariance estimation method based on the concept of information state is introduced. By this method, the impact of other sensors' transmission power on the overall transmission process is effectively accounted for. As a result, the proposed energy scheduling problem with uncertain feedback is converted into a Markov decision process (MDP) with perfect information, which becomes more amenable to analysis and solution. The Bellman dynamic programming (DP) equation is employed to obtain the optimal solution. In situations where feedback information may be missing, the relative value iteration algorithm is utilized to solve the Bellman equation, through which the optimal energy allocation strategy is derived. Ultimately, the structural results and a numerical simulation verify the performance of the proposed energy allocation policy. References | Related Articles | Metrics

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ON THE STABILITY OF A VARIABLE TIME STEP SCHEME FOR THE FERROHYDRODYNAMICS FLOW Aytura KERAM, Pengzhan HUANG, Yinnian HE Acta mathematica scientia,Series B. 2026, 46 (2):  971-992.  DOI: 10.1007/s10473-026-0223-1 Abstract ( 7 )   Save In this paper, we design a decoupled, linear, stable scheme with variable time step for solving a ferrohydrodynamics system. Based on the backward Euler scheme with variable time step for time discretization, this scheme deals with nonlinear terms by explicit treatment. Meanwhile, we show the stability of the proposed scheme. Finally, some numerical experiments are provided to illustrate the accuracy and stability of the proposed scheme. References | Related Articles | Metrics

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GENERALIZING SUBDIFFUSIVE BLACK-SCHOLES MODEL BY VARIABLE EXPONENT: MODEL TRANSFORMATION AND NUMERICAL APPROXIMATION Meihui ZHANG, Yaxue LIU, Mengmeng LIU, Wenlin QIU, Xiangcheng ZHENG Acta mathematica scientia,Series B. 2026, 46 (2):  993-1010.  DOI: 10.1007/s10473-026-0224-0 Abstract ( 10 )   Save This work generalizes the subdiffusive Black-Scholes model by introducing the variable exponent in order to provide adequate descriptions for the option pricing, where the variable exponent may account for the variation of the memory property. In addition to standard nonlinear-to-linear transformation, we apply a further spatial-temporal transformation to convert the model to a more tractable form in order to circumvent the difficulties caused by the "non-positive, non-monotonic" variable-exponent memory kernel. An interesting phenomenon is that the spatial transformation not only eliminates the advection term but naturally turns the original noncoercive spatial operator into a coercive one due to the specific structure of the Black-Scholes model, which thus avoids imposing constraints on coefficients. Then we perform numerical analysis for both the semi-discrete and fully discrete schemes to support numerical simulation. Numerical experiments are carried out to substantiate the theoretical results. References | Related Articles | Metrics

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PRIMAL HYBRID FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS WITH GRADIENT TYPE NON-LINEARITY Ravina SHOKEEN, Ajit PATEL, Divay GARG Acta mathematica scientia,Series B. 2026, 46 (2):  1011-1035.  DOI: 10.1007/s10473-026-0225-z Abstract ( 13 )   Save This article develops the primal hybrid finite element method with Lagrange multipliers to approximate nonlinear parabolic initial-boundary value problems with gradient type non-linearity.A modified elliptic projection is used to produce optimal order error estimates for the semi-discrete and backward Euler-based complete discrete schemes. In addition, error estimates in $L^{\infty}$-norm are established which are optimal in nature. Superconvergence result of the gradient in $L^{\infty}$-norm is discussed for the error between the primal hybrid solution and elliptic projection. As a bi-product, the proposed analysis provides optimal error analysis for non-conforming CR-elements.Finally, numerical tests are performed to validate the theoretical findings. References | Related Articles | Metrics

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ERRATUM TO: LOG-CONCAVITY OF THE FIRST DIRICHLET EIGENFUNCTION OF SOME ELLIPTIC DIFFERENTIAL OPERATORS AND CONVEXITY INEQUALITIES FOR THE RELEVANT EIGENVALUE Andrea COLESANTI Acta mathematica scientia,Series B. 2026, 46 (2):  1036-1036.  DOI: 10.1007/s10473-026-0226-y Abstract ( 9 )   Save Related Articles | Metrics