Reaction diffusion equations with boundary degeneracy

In this article, we consider the reaction diffusion equation $$ \frac{\partial u}{\partial t} = \Delta A(u),\quad (x,t)\in \Omega \times (0,T), $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of...

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Main Author: Huashui Zhan
Format: Article
Language:English
Published: Texas State University 2016-03-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2016/81/abstr.html
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author Huashui Zhan
author_facet Huashui Zhan
author_sort Huashui Zhan
collection DOAJ
description In this article, we consider the reaction diffusion equation $$ \frac{\partial u}{\partial t} = \Delta A(u),\quad (x,t)\in \Omega \times (0,T), $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
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spelling doaj.art-0653795bb30c469e86e3e91a6c97ccc42022-12-22T01:30:54ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-03-01201681,113Reaction diffusion equations with boundary degeneracyHuashui Zhan0 Xiamen Univ. of Technology, Fujian, China In this article, we consider the reaction diffusion equation $$ \frac{\partial u}{\partial t} = \Delta A(u),\quad (x,t)\in \Omega \times (0,T), $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.http://ejde.math.txstate.edu/Volumes/2016/81/abstr.htmlReaction diffusion equation Fichera-Oleinik theoryboundary conditiondegeneracy
spellingShingle Huashui Zhan
Reaction diffusion equations with boundary degeneracy
Electronic Journal of Differential Equations
Reaction diffusion equation
Fichera-Oleinik theory
boundary condition
degeneracy
title Reaction diffusion equations with boundary degeneracy
title_full Reaction diffusion equations with boundary degeneracy
title_fullStr Reaction diffusion equations with boundary degeneracy
title_full_unstemmed Reaction diffusion equations with boundary degeneracy
title_short Reaction diffusion equations with boundary degeneracy
title_sort reaction diffusion equations with boundary degeneracy
topic Reaction diffusion equation
Fichera-Oleinik theory
boundary condition
degeneracy
url http://ejde.math.txstate.edu/Volumes/2016/81/abstr.html
work_keys_str_mv AT huashuizhan reactiondiffusionequationswithboundarydegeneracy