Existence of entropy measure-valued solutions for forward-backward p-parabolic equations

摘要

In this paper we have proved that the Dirichlet problemfor the forward-backward p-parabolic equation has an entropy measurevaluedsolution which has been obtained as a singular limit of weaksolutions and their gradients to the Dirichlet problem for the ellipticequation containing the anisotropic (p; 2)-Laplace operator. In order toguarantee the existence of entropy measure-valued solutions, the initialand final conditions should be formulated in the form of integral inequalities.This means that an entropy measure-valued solution can deviatefrom both initial and final data on the boundary. Moreover, a gradientYoung measure appears in the representation of an entropy measurevaluedsolution. The uniqueness of entropy measure-valued solutions isstill an open question.