Displaying similar documents to “Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems.”

Existence of weak solutions to doubly degenerate diffusion equations

Aleš Matas, Jochen Merker (2012)

Applications of Mathematics

Similarity:

We prove existence of weak solutions to doubly degenerate diffusion equations u ˙ = Δ 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 Ω 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...