Degenerate parabolic initial-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

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Edge-degenerate Boundary Value Problems on Cones

We consider edge-degenerate families of pseudodiierential boundary value problems on a semi-innnite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near innnity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.

A Generalized Maximum Principle for Boundary Value Problems for Degenerate Parabolic Operators with Discontinuous Coefficients

In [14] M.G.Platone Garroni has extended the classical generalized maximum principle (see, for instance, [15]), when the coefficients of the operator are discontinuous, to subsolutions of elliptic linear second order equations with mixed type boundary unilateral conditions, that is, on a portion of the boundary ∂Ω of Ω, the values of the solution are assigned, while on the other part a unilater...