On Global Boundedness, Stability and Almost Periodicity of Solutions for Heat Equations

Abstract

This paper is concerned with the existence, stability and almost periodicity of global bounded solutions of linear and semilinear parabolic equations. We give a rather complete characterization to the linear equation u_t − Δu = λu + f(x,t), in term of the parameter λ, of whether or not the global bounded solutions exist. Also, we obtain a complete characterization on the stability of global bounded solutions.