Parabolic power concavity and parabolic boundary value problems

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

Initial - Boundary Value Problems for Parabolic Equations

Maximal regularity and quasilinear parabolic boundary value problems

∂tw +A(v)w = f(v) in J̊ , w(0) = 0 has a unique solution w = w(v) ∈W(J). Clearly, a fixed point of the map v 7→ w(v) is a solution of (1). Fixed point arguments of this type are, of course, omnipresent in the study of evolution equations of type (1). The new feature of our work, which distinguishes it from all previous investigations, is that we assume that W(J) is a maximal regularity space and...

Galerkin Approximations of Abstract Parabolic Boundary Value Problems

Galerkin approximations of an abstract parabolic boundary value problem with "rough" boundary data are considered. The optimal rates of convergence in Lp[0T; L2(ti)] norms for L [07"; L2(T)] boundary terms are derived.

Boundary Value Problems for Higher Order Parabolic Equations

We consider a constant coefficient parabolic equation of order 2m and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order m−1 lie in L2 with respect to surface measure. In addition, a regularity result for the solution is obtained if...