The Cauchy problem for time-dependent abstract parabolic equations of higher order

Abstract

After the pioneering works by Chazarain [2] and Dubinskii [3] in the early seventies, several papers were devoted to higher order differential equations in a Banach space, especially for either constant coefficient or second order equations. Detailed references can be find in [4, Sect. 25(c)]. Very recent results in the constant coefficient case are due to Sandefur [S] for second order semilinear equations and to Neubrander [S] for linear arbitrary order equations. In a recent paper [7], we considered an equation such as