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 |
| Published: |
Texas State University
2016-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/81/abstr.html |
| Summary: | 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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| ISSN: | 1072-6691 |