PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL REACTION-DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

Title & Authors
PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL REACTION-DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION
Mu, Chunlai; Liu, Dengming; Zhou, Shouming;

Abstract
In this paper, we study the properties of positive solutions for the reaction-diffusion equation $\small{u_t}$ = $\small{\Delta_u+{\int}_\Omega u^pdx-ku^q}$ in $\small{\Omega\times(0,T)}$ with nonlocal nonlinear boundary condition u (x, t) = $\small{{\int}_{\Omega}f(x,y)u^l(y,t)dy}$ $\small{\partial\Omega\times(0,T)}$ and nonnegative initial data $\small{u_0}$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.
Keywords
reaction-diffusion equation;global existence;blow-up;nonlocal nonlinear boundary condition;
Language
English
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