Enrico Obrecht

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

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

The Laplacian with Generalized Wentzell Boundary Conditions

The regularity of the solutions of the heat equation

Conditions for parabolicity of second order abstract differential equations

\frac{{\partial u}}{{\partial t}} = \Delta u

Structure of solutions to linear evolution equations : Extensions of d'Alembert's formula

with suitable boundary conditions in different types of function spaces is an impor-tant issue in many applications to problems coming from Physics and Engineering.