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  • We prove existence of weak solutions to doubly degenerate diffusion equations $\dot{u}=\Delta_p u^{m-1}+f$ $(m,p\ge2)$ 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 $\Omega\subset\mathbb R^n$ 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.
  • We prove existence of weak solutions to doubly degenerate diffusion equations $\dot{u}=\Delta_p u^{m-1}+f$ $(m,p\ge2)$ 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 $\Omega\subset\mathbb R^n$ 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. (en)
Title
  • Existence of weak solutions to doubly degenerate diffusion equations
  • Existence of weak solutions to doubly degenerate diffusion equations (en)
skos:prefLabel
  • Existence of weak solutions to doubly degenerate diffusion equations
  • Existence of weak solutions to doubly degenerate diffusion equations (en)
skos:notation
  • RIV/49777513:23520/12:43914914!RIV13-MSM-23520___
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  • Z(MSM4977751301)
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  • 1
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  • 135451
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  • RIV/49777513:23520/12:43914914
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  • p-Laplacian, doubly nonlinear evolution equation, weak solution (en)
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  • CZ - Česká republika
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  • [DB5519DF9271]
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  • Applications of Mathematics
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  • 57
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  • Matas, Aleš
  • Merker, Jochen
http://linked.open...ain/vavai/riv/wos
  • 000302094000004
http://linked.open...n/vavai/riv/zamer
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  • 0862-7940
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  • 23520
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