Abstract:

This article studies the Cauchy problem for a class of doubly nonlinear degenerate parabolic equations $\frac{\partial u}{\partial t}={\rm div}(A(|\nabla{B}(u)|)\nabla{B}(u)).$ Under certain conditions, the author considers its regularized problem and establishes some estimates. On the basis of the estimates, the existence and uniqueness of the generalized solutions in BV space are proved.

Key words: Degenerate parabolic equation, generalized solution, existence, uniqueness