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Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density
Random dispersal vs. nonlocal dispersal
1.  Department of Mathematics, The Ohio State University, Columbus, OH 43210 
2.  Department of Mathematics, The Ohio State State University, Columbus, Ohio 43210 
3.  Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849 
[1] 
Henri Berestycki, Nancy Rodríguez. A nonlocal bistable reactiondiffusion equation with a gap. Discrete & Continuous Dynamical Systems  A, 2017, 37 (2) : 685723. doi: 10.3934/dcds.2017029 
[2] 
Abraham Solar. Stability of nonmonotone and backward waves for delay nonlocal reactiondiffusion equations. Discrete & Continuous Dynamical Systems  A, 2019, 39 (10) : 57995823. doi: 10.3934/dcds.2019255 
[3] 
Zhenguo Bai, Tingting Zhao. Spreading speed and traveling waves for a nonlocal delayed reactiondiffusion system without quasimonotonicity. Discrete & Continuous Dynamical Systems  B, 2018, 23 (10) : 40634085. doi: 10.3934/dcdsb.2018126 
[4] 
Chris Cosner. Reactiondiffusionadvection models for the effects and evolution of dispersal. Discrete & Continuous Dynamical Systems  A, 2014, 34 (5) : 17011745. doi: 10.3934/dcds.2014.34.1701 
[5] 
Nancy Azer, P. van den Driessche. Competition and Dispersal Delays in Patchy Environments. Mathematical Biosciences & Engineering, 2006, 3 (2) : 283296. doi: 10.3934/mbe.2006.3.283 
[6] 
Shouming Zhou, Chunlai Mu, Yongsheng Mi, Fuchen Zhang. Blowup for a nonlocal diffusion equation with exponential reaction term and Neumann boundary condition. Communications on Pure & Applied Analysis, 2013, 12 (6) : 29352946. doi: 10.3934/cpaa.2013.12.2935 
[7] 
ShiLiang Wu, WanTong Li, SanYang Liu. Exponential stability of traveling fronts in monostable reactionadvectiondiffusion equations with nonlocal delay. Discrete & Continuous Dynamical Systems  B, 2012, 17 (1) : 347366. doi: 10.3934/dcdsb.2012.17.347 
[8] 
Kazuhisa Ichikawa, Mahemauti Rouzimaimaiti, Takashi Suzuki. Reaction diffusion equation with nonlocal term arises as a mean field limit of the master equation. Discrete & Continuous Dynamical Systems  S, 2012, 5 (1) : 115126. doi: 10.3934/dcdss.2012.5.115 
[9] 
Donald L. DeAngelis, Bo Zhang. Effects of dispersal in a nonuniform environment on population dynamics and competition: A patch model approach. Discrete & Continuous Dynamical Systems  B, 2014, 19 (10) : 30873104. doi: 10.3934/dcdsb.2014.19.3087 
[10] 
WanTong Li, Li Zhang, GuoBao Zhang. Invasion entire solutions in a competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems  A, 2015, 35 (4) : 15311560. doi: 10.3934/dcds.2015.35.1531 
[11] 
Song Liang, Yuan Lou. On the dependence of population size upon random dispersal rate. Discrete & Continuous Dynamical Systems  B, 2012, 17 (8) : 27712788. doi: 10.3934/dcdsb.2012.17.2771 
[12] 
Tomás Caraballo, José A. Langa, James C. Robinson. Stability and random attractors for a reactiondiffusion equation with multiplicative noise. Discrete & Continuous Dynamical Systems  A, 2000, 6 (4) : 875892. doi: 10.3934/dcds.2000.6.875 
[13] 
Yuncheng You. Random attractors and robustness for stochastic reversible reactiondiffusion systems. Discrete & Continuous Dynamical Systems  A, 2014, 34 (1) : 301333. doi: 10.3934/dcds.2014.34.301 
[14] 
GuoBao Zhang, Ruyun Ma, XueShi Li. Traveling waves of a LotkaVolterra strong competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 587608. doi: 10.3934/dcdsb.2018035 
[15] 
S.A. Gourley, Yang Kuang. TwoSpecies Competition with High Dispersal: The Winning Strategy. Mathematical Biosciences & Engineering, 2005, 2 (2) : 345362. doi: 10.3934/mbe.2005.2.345 
[16] 
Georg Hetzer, Tung Nguyen, Wenxian Shen. Coexistence and extinction in the VolterraLotka competition model with nonlocal dispersal. Communications on Pure & Applied Analysis, 2012, 11 (5) : 16991722. doi: 10.3934/cpaa.2012.11.1699 
[17] 
Badr Saad T. Alkahtani, Ilknur Koca. A new numerical scheme applied on revisited nonlinear model of predatorprey based on derivative with nonlocal and nonsingular kernel. Discrete & Continuous Dynamical Systems  S, 2020, 13 (3) : 429442. doi: 10.3934/dcdss.2020024 
[18] 
Keyan Wang. Global wellposedness for a transport equation with nonlocal velocity and critical diffusion. Communications on Pure & Applied Analysis, 2008, 7 (5) : 12031210. doi: 10.3934/cpaa.2008.7.1203 
[19] 
Qiyu Jin, Ion Grama, Quansheng Liu. Convergence theorems for the NonLocal Means filter. Inverse Problems & Imaging, 2018, 12 (4) : 853881. doi: 10.3934/ipi.2018036 
[20] 
Gabriel Peyré, Sébastien Bougleux, Laurent Cohen. Nonlocal regularization of inverse problems. Inverse Problems & Imaging, 2011, 5 (2) : 511530. doi: 10.3934/ipi.2011.5.511 
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