Electron. J. Diff. Equ., Vol. 2016 (2016), No. 81, pp. 1-13.

Reaction diffusion equations with boundary degeneracy

Huashui Zhan

Abstract:
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.

Submitted May 14, 2015. Published March 23, 2016.
Math Subject Classifications: 35L65, 35K85, 35R35.
Key Words: Reaction diffusion equation; Fichera-Oleinik theory; boundary condition; degeneracy.

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Huashui Zhan
School of Applied Mathematics
Xiamen University of Technology
Xiamen, Fujian 361024, China
email: 2012111007@xmut.edu.cn

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