Blow-up Rate Estimates and Blow-up Set for a System of Two Heat Equations with Coupled Nonlinear Neumann Boundary Conditions
Abstract
This paper deals with the blow-up properties of positive solutions to a parabolicsystem of two heat equations, defined on a ball in associatedwith coupledNeumann boundary conditions of exponential type. The upper bounds of blow-uprate estimates are derived. Moreover, it is proved that the blow-up in this problemcan only occur on the boundary.
Keywords
Heat equation, Neumann boundary conditions, Blow-up set, Blow-up rate estimate, Green function.Metrics