The absence of global positive solutions to semilinear parabolic differential inequalities in exterior domain

Abstract

We are concerned with the absence of global positive solutions to certain semi-linear parabolic differential inequalities in exterior domains with nontrivial boundary condition. Assuming that the boundary value is positive, we determine the critical value of the exponent of a nonlinear term, which is responsible for the nonexistence of a solution. In the case of vanishing boundary value, the critical exponent was previously found by G. Laptev (2003) and has a smaller value.