曲率控制细胞和组织生长演化模型的Cauchy问题

Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (3): 771-784.

Previous Articles Next Articles

Cauchy Problem for the Evolution of Cells and Tissue During Curvature-Controlled Growth

Wang Zenggui()

School of Mathematical Sciences, Liaocheng University, Shandong Liaocheng 252059

Received:2022-03-22 Revised:2023-01-12 Online:2023-06-26 Published:2023-06-01
Contact: Zenggui Wang E-mail:wangzenggui@lcu.edu.cn
Supported by:
Natural Science Foundation of Shandong Province(ZR2021MA084);Scientific Research Foundation of Liaocheng University(318012025);Discipline with Strong Characteristics of Liaocheng University-Intelligent Science and Technology(319462208)

Abstract

Abstract:

In this paper, We consider Cauchy problem for the evolution of cells and tissue during curvature-controlled growth. By the definition of Riemann invariants, the evolution equation can be rewritten as a non-homogeneous quasilinear hyperbolic system. the lifespan of classical solution to the initial value problem is given by a priori estimation of the solution of the quasilinear hyperbolic system.

Key words: The evolution of cells and tissue during curvature-controlled growth, Non-homogeneous quasilinear hyperbolic system, Priori estimation, Lifespan

CLC Number:

O175.2

Wang Zenggui. Cauchy Problem for the Evolution of Cells and Tissue During Curvature-Controlled Growth[J].Acta mathematica scientia,Series A, 2023, 43(3): 771-784.

Trendmd

References

[1]	Alias M A, Buenzli P R. Modeling the effect of curvature on the collective behavior of cells growing wew tissue. Biophysical Journal, 2017, 112(1): 193-204
[2]	Alias M A, Buenzli P R. Osteoblasts infill irregular pores under curvature and porosity controls: a hypothesis-testing analysis of cell behaviours. Biomechanics and Modeling in Mechanobiology, 2018, 17(5): 1357-1371
[3]	Alias M A, Buenzli P R. A level-set method for the evolution of cells and tissue during curvature-controlled growth. International Journal for Numerical Methods in Biomedical Engineering, 2020, 36(1): e3279
[4]	Gurtin M E, Podio-Guidugli P. A hyperbolic theory for the evolution of plane curves. SIAM J Math Anal, 1991, 22: 575-586
[5]	Rotstein H G, Brandon S, Novick-Cohen A. Hyperbolic flow by mean curvature. Journal of Crystal Growth, 1999, 198-199: 1256-1261
[6]	Yau S T. Review of geometry and analysis. Asian J Math, 2000, 4: 235-278
[7]	LeFloch P G, Smoczyk K. The hyperbolic mean curvature flow. Journal De Mathématiques Pures et Appliqués, 2009, 90(6): 591-684
[8]	李秀展, 王增桂. 双曲平均曲率流Cauchy问题经典解的生命跨度. 中国科学: 数学, 2017, 47(8): 953-968
[8]	Li X Z, Wang Z G. The lifespan of classical solution to the cauchy problem for the hyperbolic mean curvature flow. Sci Sin Math, 2017, 47(8): 953-968
[9]	LeFloch P G, Yan W P. Nonlinear stability of blow-up solutions to the hyperbolic mean curvature flow. J Differential Equations, 2020, 269(10): 8269-8307
[10]	He C L, Kong D X, Liu K F. Hyperbolic mean curvature flow. J. Differential Equations, 2009, 246: 373-390
[11]	Kong D X, Liu K F, Wang Z G. Hyperbolic mean curvature flow: Evolution of plane curves. Acta Mathematica Scientia (A special issue dedicated to Professor Wu Wenjun's 90th birthday), 2009, 29: 493-614
[12]	Kong D X, Wang Z G. Formation of singularities in the motion of plane curves under hyperbolic mean curvature flow. J Differential Equations, 2009, 247: 1694-1719
[13]	He C L, Huang S J, Xing X M. Self-similar solutions to the hyperbolic mean curvature flow. Acta Mathematica Scientia, 2017, 37B(3): 657-667
[14]	Wang Z G. Hyperbolic mean curvature flow with a forcing term: evolution of plane curves. Nonlinear Analysis: Theory, Methods and Applications, 2014, 97: 65-82
[15]	Wang Z G. Symmetries and solutions of hyperbolic mean curvature flow with a constant forcing term. Applied Mathematics and Computation, 2014, 235: 560-566
[16]	王增桂. 带有线性外力场的双曲平均曲率流Cauchy问题经典解的生命跨度. 中国科学:数学, 2013, 43(12): 1193-1208
[16]	Wang Z G. The lifespan of classical solution to the Cauchy problem for the hyperbolic mean curvature flow with a linear forcing term. Sci Sin Math, 2013, 43(12): 1193-1208
[17]	Wang Z G. Hyperbolic mean curvature flow in Minkowski space. Nonlinear Analysis: Theory, Methods and Applications, 2014, 94: 259-271
[18]	Mao J. Forced hyperbolic mean curvature flow. Kodai Mathematical Journal, 2012, 35(3): 500-522
[19]	Mao J, Wu C X, Zhou Z. Hyperbolic inverse mean curvature flow. Czechoslovak Mathematical Journal, 2019, (2019): 1-34
[20]	Zhou Z, Wu C X, Mao J. Hyperbolic curve flows in the plane. Journal of Inequalities and Applications, 2019, 2019(1): 1-17
[21]	Wang Z G. Life-span of classical solutions to hyperbolic inverse mean curvature flow. Discrete Dynamics in Nature and Society, 2020, 2020: 1-12
[22]	Chou K S, Wo W F. On hyperbolic Gauss curvature flows. J Diff Geom, 2011, 89(3): 455-486
[23]	Wo W F, Ma F Y, Qu C Z. A hyperbolic-type affine invariant curve flow. Communications in Analysis and Geometry, 2014, 22(2): 219-245
[24]	Wang Z G. A dissipative hyperbolic affine flow. Journal of Mathematical Analysis and Applications, 2018, 465(2): 1094-1111
[25]	Notz T. Closed Hypersurfaces Driven by their Mean Curvature and Inner Pressure[D]. Berlin: AlbertEinstein-Institut, 2010
[26]	Yan W P. Motion of closed hypersurfaces in the central force fields. J Differential Equations, 2016, 261(3): 1973-2005
[27]	Ta-Tsien L, Wen-Ci Y. Boundary Value Problems for Quasilinear Hyperbolic Systems. Carolina: Duke Univ, 1985

Cauchy Problem for the Evolution of Cells and Tissue During Curvature-Controlled Growth

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 7

Metrics

Comments

Recommended 0

[1]	Baiping Ouyang,Shengzhong Xiao. Nonexistence of Global Solutions for a Semilinear Double-Wave Equation with a Nonlinear Memory Term [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1372-1381.
[2]	Jinglei Zhao,Jiacheng Lan,Shanshan Yang. Lifespan Estimate of Damped Semilinear Wave Equation in Exterior Domain with Neumann Boundary Condition [J]. Acta mathematica scientia,Series A, 2021, 41(4): 1033-1041.
[3]	Shoujun Huang,Xiwang Meng. Improved Ordinary Differential Inequality and Its Application to Semilinear Wave Equations [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1319-1332.
[4]	Hongbiao Jiang,Haihang Wang. Lifespan Estimation of Solutions to Cauchy Problem of Semilinear Wave Equation [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1146-1157.
[5]	Duan Shuangshuang, Huang Shoujun. Blow up of Periodic Solutions for a Class of Keller-Segel Equations Arising in Biology [J]. Acta mathematica scientia,Series A, 2017, 37(2): 326-341.
[6]	Geng Jinbo, Yang Zhenzhen, Lai Ning-An. Blow up and Lifespan Estimates for Initial Boundary Value Problem of Semilinear Schrödinger Equations on Half-Life [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1186-1195.
[7]	Zhang Quande. On Global Existence,Blow Up and Life Span of Nonlinear Hyperbolic Equations [J]. Acta mathematica scientia,Series A, 1999, 19(1): 45-52.