Existence of weak solutions to doubly degenerate diffusion equations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F12%3A43914914" target="_blank" >RIV/49777513:23520/12:43914914 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Existence of weak solutions to doubly degenerate diffusion equations

Original language description

We prove existence of weak solutions to doubly degenerate diffusion equations $dot{u}=Delta_p u^{m-1}+f$ $(m,pge2)$ by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstractsetting, which allows to choose function spaces corresponding to bounded or unbounded domains $Omegasubsetmathbb R^n$ 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2012

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Applications of Mathematics

ISSN

0862-7940

e-ISSN

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Volume of the periodical

57

Issue of the periodical within the volume

1

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

26

Pages from-to

43-69

UT code for WoS article

000302094000004

EID of the result in the Scopus database

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