Boundary Value Problem for Quasilinear Degenerate Parabolic Equations.

摘要

Using the theory of functions of bounded variation, Vol'pert and Hudjaev successfully treated the initial-value problem for a class of degenerate parabolic equations in one space dimension. Of particular interest was their ability to incorporate even the completely degenerate case of a scalar conservation law in the class they treated. The author subsequently treated the first boundary value problem in a similar spirit and generality. The current work shows that analogous results can be obtained for other boundary conditions. As before, regularizatio is used to obtain existence results for approximate problems. New estimates are obtained on the approximations which allow passage to the limit.