American Institute of Mathematical Sciences

Advanced
January  2008, 9(1): 65-73. doi: 10.3934/dcdsb.2008.9.65

On a nonlocal reaction-diffusion population model

Keng Deng 1,

1. 

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010

Received  January 2007 Revised  August 2007 Published  October 2007

In this paper, we consider a nonlocal parabolic initial value problem that models a single species which is diffusing, aggregating, reproducing and competing for space and resources. We establish a comparison principle and construct monotone sequences to show the existence and uniqueness of the solution to the problem. We also analyze the long-time behavior of the solution.
Keywords: monotone sequences, permanence., Nonlocal population model, existence-uniqueness, comparison principle.
Mathematics Subject Classification: 35A05, 35B40, 35K57, 92D2.
Citation: Keng Deng. On a nonlocal reaction-diffusion population model. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 65-73. doi: 10.3934/dcdsb.2008.9.65
[1]

Daoyi Xu, Weisong Zhou. Existence-uniqueness and exponential estimate of pathwise solutions of retarded stochastic evolution systems with time smooth diffusion coefficients. Discrete & Continuous Dynamical Systems, 2017, 37 (4) : 2161-2180. doi: 10.3934/dcds.2017093
[2]

Qi Yao, Linshan Wang, Yangfan Wang. Existence-uniqueness and stability of the mild periodic solutions to a class of delayed stochastic partial differential equations and its applications. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4727-4743. doi: 10.3934/dcdsb.2020310
[3]

Hongfu Yang, Xiaoyue Li, George Yin. Permanence and ergodicity of stochastic Gilpin-Ayala population model with regime switching. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3743-3766. doi: 10.3934/dcdsb.2016119
[4]

Christel Geiss, Alexander Steinicke. Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting. Probability, Uncertainty and Quantitative Risk, 2018, 3 (0) : 9-. doi: 10.1186/s41546-018-0034-y
[5]

Christel Geiss, Alexander Steinicke. Correction to: “Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting”. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 6-. doi: 10.1186/s41546-019-0040-8
[6]

Xin Xu. Existence of monotone positive solutions of a neighbour based chemotaxis model and aggregation phenomenon. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4327-4348. doi: 10.3934/cpaa.2020195
[7]

Xin Lai, Xinfu Chen, Mingxin Wang, Cong Qin, Yajing Zhang. Existence, uniqueness, and stability of bubble solutions of a chemotaxis model. Discrete & Continuous Dynamical Systems, 2016, 36 (2) : 805-832. doi: 10.3934/dcds.2016.36.805
[8]

C. Kopf. Symbol sequences and entropy for piecewise monotone transformations with discontinuities. Discrete & Continuous Dynamical Systems, 2000, 6 (2) : 299-304. doi: 10.3934/dcds.2000.6.299
[9]

Peixuan Weng, Xiao-Qiang Zhao. Spatial dynamics of a nonlocal and delayed population model in a periodic habitat. Discrete & Continuous Dynamical Systems, 2011, 29 (1) : 343-366. doi: 10.3934/dcds.2011.29.343
[10]

Bang-Sheng Han, Zhi-Cheng Wang. Traveling wave solutions in a nonlocal reaction-diffusion population model. Communications on Pure & Applied Analysis, 2016, 15 (3) : 1057-1076. doi: 10.3934/cpaa.2016.15.1057
[11]

Yueding Yuan, Zhiming Guo, Moxun Tang. A nonlocal diffusion population model with age structure and Dirichlet boundary condition. Communications on Pure & Applied Analysis, 2015, 14 (5) : 2095-2115. doi: 10.3934/cpaa.2015.14.2095
[12]

Timothy Blass, Rafael De La Llave, Enrico Valdinoci. A comparison principle for a Sobolev gradient semi-flow. Communications on Pure & Applied Analysis, 2011, 10 (1) : 69-91. doi: 10.3934/cpaa.2011.10.69
[13]

Michele V. Bartuccelli, S.A. Gourley, Y. Kyrychko. Comparison and convergence to equilibrium in a nonlocal delayed reaction-diffusion model on an infinite domain. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1015-1026. doi: 10.3934/dcdsb.2005.5.1015
[14]

Zhiming Guo, Zhi-Chun Yang, Xingfu Zou. Existence and uniqueness of positive solution to a non-local differential equation with homogeneous Dirichlet boundary condition---A non-monotone case. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1825-1838. doi: 10.3934/cpaa.2012.11.1825
[15]

Inger Daniels, Catherine Lebiedzik. Existence and uniqueness of a structural acoustic model involving a nonlinear shell. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 243-252. doi: 10.3934/dcdss.2008.1.243
[16]

Stefanie Hirsch, Dietmar Ölz, Christian Schmeiser. Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 4945-4962. doi: 10.3934/dcds.2016014
[17]

T. Tachim Medjo. On the existence and uniqueness of solution to a stochastic simplified liquid crystal model. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2243-2264. doi: 10.3934/cpaa.2019101
[18]

Hiroshi Matano, Yoichiro Mori. Global existence and uniqueness of a three-dimensional model of cellular electrophysiology. Discrete & Continuous Dynamical Systems, 2011, 29 (4) : 1573-1636. doi: 10.3934/dcds.2011.29.1573
[19]

Telma Silva, Adélia Sequeira, Rafael F. Santos, Jorge Tiago. Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 343-362. doi: 10.3934/dcdss.2016.9.343
[20]

Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707-725. doi: 10.3934/krm.2009.2.707

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (79)
  • HTML views (0)
  • Cited by (14)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences