On Blow-up set of a Semilinear Heat Equation with Neumann Boundary Condition

Abstract

This paper deals with the blow-up set of a semilinear heat equation defined on a ball, with nonlinear boundary condition, where the reaction term and the boundary term are powers of exponential types. In [9], under some restricted assumption, it has been proved that, in case of, the nonlinear terms are of exponential types without powers, the blow-up occurs only on the boundary. Our aim is to extend that result, for some regains of the powers those appear on the reaction and boundary terms.