Existence of weak solutions to doubly degenerate diffusion equations View Full Text


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Article Info

DATE

2012-02

AUTHORS

Aleš Matas, Jochen Merker

ABSTRACT

We prove existence of weak solutions to doubly degenerate diffusion equations 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 ⊂ ℝn 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. More... »

PAGES

43-69

References to SciGraph publications

  • 1986-12. Compact sets in the spaceLp(O,T; B) in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • 2003-07. Uniqueness for nonlinear degenerate problems in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 1997-01. Regularity for doubly nonlinear parabolic equations in JOURNAL OF MATHEMATICAL SCIENCES
  • 1993. Degenerate Parabolic Equations in NONE
  • 1983-09. Quasilinear elliptic-parabolic differential equations in MATHEMATISCHE ZEITSCHRIFT
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    http://scigraph.springernature.com/pub.10.1007/s10492-012-0004-0

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    http://dx.doi.org/10.1007/s10492-012-0004-0

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