Articles

BLOW-UP IN A FRACTIONAL LAPLACIAN MUTUALISTIC MODEL WITH NEUMANN BOUNDARY CONDITIONS

  • Chao Jiang ,
  • Zuhan Liu ,
  • Ling Zhou
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  • School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

Received date: 2021-03-24

  Revised date: 2022-05-30

  Online published: 2022-11-02

Supported by

The work was partially supported by National Natural Science Foundation of China (11771380) and Natural Science Foundation of Jiangsu Province (BK20191436).

Abstract

In this paper, a fractional Laplacian mutualistic system under Neumann boundary conditions is studied. Using the method of upper and lower solutions, it is proven that the solutions of the fractional Laplacian strong mutualistic model with Neumann boundary conditions will blow up when the intrinsic growth rates of species are large.

Cite this article

Chao Jiang , Zuhan Liu , Ling Zhou . BLOW-UP IN A FRACTIONAL LAPLACIAN MUTUALISTIC MODEL WITH NEUMANN BOUNDARY CONDITIONS[J]. Acta mathematica scientia, Series B, 2022 , 42(5) : 1809 -1816 . DOI: 10.1007/s10473-022-0506-0

References

[1] Abatangelo N. A remark on nonlocal Neumann conditions for the fractional Laplacian. Arch Math (Basel), 2020, 114(6): 699–708
[2] Barrios B, Montoro L, Peral I, Soria F. Neumann conditions for the higher order s-fractional Laplacian (-Δ)su with s > 1. Nonlinear Anal TMA, 2020, 193: 111368
[3] Bahrouni S, Salort A M. Neumann and Robin type boundary conditions in fractional Orlicz-Sobolev spaces. ESAIM Control Optim Calc Var, 2021, 27: S15
[4] Bucur C, Valdinoci E. Nonlocal Diffusion and Applications. Springer, 2016
[5] Dipierro S, Proietti Lippi E, Valdinoci E. Linear theory for a mixed operator with Neumann conditions. Asymptot Anal, 2021, Pre-press: 1–24
[6] Dipierro S, Ros-Oton X, Valdinoci E. Nonlocal problems with Neumann boundary conditions. Rev Mat Iberoam, 2017, 33(2): 377–416
[7] Del Pezzo L M, Rossi J, Saintier N, Salort A. An optimal mass transport approach for limits of eigenvalue problems for the fractional p-Laplacian. Adv Nonlinear Anal, 2015, 4(3): 235–249
[8] Del Pezzo L M, Salort A M. The first non-zero Neumann p-fractional eigenvalue. Nonlinear Anal TMA, 2015, 118: 130–143
[9] Del Pezzo L M, Rossi J D, Salort A M. Fractional eigenvalue problems that approximate Steklov eigenvalue problems. Proc Roy Soc Edinburgh Sect A, 2018, 148(3): 499–516
[10] Du Q, Gunzburger M, Lehoucq R B, Zhou K. A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Math Models Methods Appl Sci, 2013, 23(3): 493–540
[11] Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker’s guide to the fractional Sobolev spaces. Bull Sci Math, 2012, 136(5): 521–573
[12] Granero-Belinchón R. On a drift-diffusion system for semiconductor devices. Ann Henri poincaré, 2016, 17(12): 3474–3498
[13] Jiang K R, Ling Z, Liu Z H. Global existence and asymptotic behavior of the fractional chemotaxis system with signal-dependent sensitivity. Comput Math Appl, 2019, 78(10): 3450–3470
[14] Mizoguchi N. Global existence for the Cauchy problem of the parabolic-parabolic Keller-Segel system on the plane. Calc Var Partial Differential Equations, 2013, 48(3/4): 491–505
[15] Mugnai D, Proietti Lippi E. Neumann fractional p-Laplacian: eigenvalues and existence results. Nonlinear Anal TMA, 2019, 188: 455–474
[16] Mugnai D, Proietti Lippi E. Linking over cones for the Neumann fractional p-Laplacian. J Differential Equations, 2021, 271: 797–820
[17] Mugnai D, Pinamonti A, Vecchi E. Towards a Brezis-Oswald-type result for fractional problems with Robin boundary conditions. Calc Var Partial Differential Equations, 2020, 59 (2): art 43
[18] Mugnai D, Perera K, Proietti Lippi E. A priori estimates for the fractional p-Laplacian with nonlocal Neumann boundary conditions and applications. Comm Pure Appl Anal, 2022, 21(1): 275–292
[19] Pao C V. Nonlinear Parabolic and Elliptic Equations. New York: Plenum Press, 1992
[20] Silvestre L. Regularity of the obstacle problem for a fractional power of the Laplace operator. Comm Pure Appl Math, 2007, 60(1): 67–112
[21] Wang P Y, Niu P C. A priori bounds and existence of positive solutions for weighted fractional systems. Acta Math Sci, 2021, 41B(5): 1547–1568
[22] Youssfi A, Ould Mohamed Mahmoud G. On singular equations involving fractional Laplacian. Acta Math Sci, 2020, 40B(5): 1289–1315
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