EXISTENCE OF WEAK SOLUTIONS TO DOUBLY DEGENERATE DIFFUSION EQUATIONS

We prove existence of weak solutions to doubly degenerate diffusion equations (u) over dot = Delta(p)u(m-1) + f (m,p >= 2) by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains Omega subset of R-n with Dirichlet or Neumann boundary conditions. The function f can be an inhomogeneity or a nonlinearity involving terms of the form f (u) or div(F (u)). In the appendix, an introduction to weak differentiability of functions with values in a Banach space appropriate for doubly nonlinear evolution equations is given.