TY - JOUR
T1 - Strong solutions and instability for the fitness gradient system in evolutionary games between two populations
AU - Xu, Qiuju
AU - Belmonte, Andrew
AU - deForest, Russ
AU - Liu, Chun
AU - Tan, Zhong
N1 - Funding Information:
Qiuju Xu would like to express her gratitude to Department of Mathematics of Pennsylvania State University for all the hospitality and help during her visit. She would like to thank Tai-Chia Lin, Tao Huang and Yong Wang for many fruitful discussions. In this research, Andrew Belmonte is partially supported by National Science Foundation, Grant CMMI-1463482. Chun Liu is partially supported by National Science Foundation, Grants DMS-141200 and DMS-1216938. Zhong Tan is partially supported by the National Natural Science Foundation of China (Nos. 11271305, 11531010).
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/4/5
Y1 - 2017/4/5
N2 - In this paper, we study a fitness gradient system for two populations interacting via a symmetric game. The population dynamics are governed by a conservation law, with a spatial migration flux determined by the fitness. By applying the Galerkin method, we establish the existence, regularity and uniqueness of global solutions to an approximate system, which retains most of the interesting mathematical properties of the original fitness gradient system. Furthermore, we show that a Turing instability occurs for equilibrium states of the fitness gradient system, and its approximations.
AB - In this paper, we study a fitness gradient system for two populations interacting via a symmetric game. The population dynamics are governed by a conservation law, with a spatial migration flux determined by the fitness. By applying the Galerkin method, we establish the existence, regularity and uniqueness of global solutions to an approximate system, which retains most of the interesting mathematical properties of the original fitness gradient system. Furthermore, we show that a Turing instability occurs for equilibrium states of the fitness gradient system, and its approximations.
UR - http://www.scopus.com/inward/record.url?scp=85008154390&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85008154390&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2016.12.008
DO - 10.1016/j.jde.2016.12.008
M3 - Article
AN - SCOPUS:85008154390
SN - 0022-0396
VL - 262
SP - 4021
EP - 4051
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 7
ER -