Persistence of bounded solutions of parabolic equations under domain perturbation.

The aim of this paper is to study the behavior of bounded solutions of parabolic equations on the whole real line under perturbation of the underlying domain. We give the convergence of bounded solutions of linear parabolic equations in the L and the L-settings. For the L-theory, we also prove the Hölder regularity of bounded solutions with respect to time. In addition, we study the persistence of a class of bounded solutions which decay to zero at t → ±∞ of semilinear parabolic equations under domain perturbation. [ABSTRACT FROM AUTHOR]