On the existence of a global classical solution of the boundary value problem for □u−μu+aum=0 in the interior domain

Abstract

In this paper we consider the boundary value problem for a semilinear equation □ u(t,x) - μu(t,x) + au m (t, x) = 0, μ > 0, a ∈ R in the interior domain. We find a time global classical solution with exponential decay property by using singular hyperbolic equation.