Blow-up of Solutions for a Reaction-diffusion Equation with Nonlinear Nonlocal Boundary Condition
Sen Zhou
Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing, 210023, China and College of Sciences, China Pharmaceutical University, Jiangsu Nanjing, 211198, China.
Zuodong Yang *
College of Sciences, China Pharmaceutical University, Jiangsu Nanjing, 211198, China and School of Teacher Education, Nanjing Normal University, Jiangsu Nanjing, 210097, China.
*Author to whom correspondence should be addressed.
Abstract
This paper deals with a reaction-diffusion equation subject to nonlinear nonlocal boundary condition and with nonlocal reaction source. We investigate the global existence and blow up in finite time of a nonnegative solution by using a sub-super solution method.
Keywords: Reaction-diffusion equation, nonlocal source, nonlinear nonlocal boundary condition, blow-up, global solution.