About: Existence of weak solutions to doubly degenerate diffusion equations

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Description	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___
http://linked.open...avai/predkladatel	Fakulta aplikovaných věd
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM4977751301)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Matas, Aleš
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Západočeská univerzita v Plzni / Fakulta aplikovaných věd
http://linked.open...dnocenehoVysledku	135451
http://linked.open...ai/riv/idVysledku	RIV/49777513:23520/12:43914914
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	p-Laplacian, doubly nonlinear evolution equation, weak solution (en)
http://linked.open.../riv/klicoveSlovo	p-Laplacian weak solution doubly nonlinear evolution equation
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[DB5519DF9271]
http://linked.open...i/riv/nazevZdroje	Applications of Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	57
http://linked.open...iv/tvurceVysledku	Matas, Aleš Merker, Jochen
http://linked.open...ain/vavai/riv/wos	000302094000004
http://linked.open...n/vavai/riv/zamer	Spojité a diskrétní matematické struktury a vývoj odpovídajících metod jejich zkoumání
issn	0862-7940
number of pages	26 (xsd:int)
http://localhost/t...ganizacniJednotka	23520
is http://linked.open...avai/riv/vysledek of	Existence of weak solutions to doubly degenerate diffusion equations

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