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Displaying similar documents to “A generalization of the Lions-Temam compact imbedding theorem”

Existence of weak solutions to doubly degenerate diffusion equations

Aleš Matas, Jochen Merker (2012)

Applications of Mathematics

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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...