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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Format: | Article |
Language: | English |
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Texas State University
2016-03-01
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Series: | Electronic Journal of Differential Equations |
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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. |
first_indexed | 2024-12-10T22:35:46Z |
format | Article |
id | doaj.art-0653795bb30c469e86e3e91a6c97ccc4 |
institution | Directory Open Access Journal |
issn | 1072-6691 |
language | English |
last_indexed | 2024-12-10T22:35:46Z |
publishDate | 2016-03-01 |
publisher | Texas State University |
record_format | Article |
series | Electronic Journal of Differential Equations |
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 |