On Well-posedness of Impulsive Problems for Nonlinear Parabolic Equations

Abstract

In this paper we give weaker conditions for well-posedness of impulsive problems for nonlinear parabolic equations, including existence, uniqueness and continuous dependence, even in case their corresponding Cauchy problems do not have global solutions. With some concrete examples of PDEs we show when their impulsive problems are well-posed and how the well-posedness is related to life-span of PDEs. We also indicate that some assumptions in [6] and [9] are unnecessary.