Nonnegative solutions to time fractional Keller-Segel system

被引:6
作者
Aruchamy, Akilandeeswari [1 ]
Tyagi, Jagmohan [1 ]
机构
[1] Indian Inst Technol Gandhinagar, Discipline Math, Gandhinagar, India
关键词
a priori estimates; existence theory; fractional parabolic system; Galerkin approximation method; Keller-Segel system; weak solutions; PARABOLIC CHEMOTAXIS-SYSTEM; BLOW-UP; GLOBAL-SOLUTIONS; ASYMPTOTIC-BEHAVIOR; DIFFUSION EQUATION; MODEL; BOUNDEDNESS; EXISTENCE; DEFINITION;
D O I
10.1002/mma.6880
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We establish the existence of nonnegative weak solutions to time fractional Keller-Segel system with Dirichlet boundary condition in a bounded domain with smooth boundary. Since the considered system has a cross-diffusion term and the corresponding diffusion matrix is not positive definite, we first regularize the system. Then under suitable assumptions on the initial conditions, we establish the existence of solutions to the system by using the Galerkin approximation method. The convergence of solutions is proved by means of compactness criteria for fractional partial differential equations. The nonnegativity of solutions is proved by the standard arguments. Furthermore, the existence of the weak solution to the system with Neumann boundary condition is discussed.
引用
收藏
页码:1812 / 1830
页数:19
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