Abstract: The bistable reaction-diffusion-convection equation\del_t u + \nabla \cdot \bff(u) = -{1\over\e}g(u) +\e\Delta u, \quad x\in\RR^n, \ u\in\RR\leqno(1)is considered. Stationary traveling waves of above equation are proved to exist when $f(u)$ is symmetric and $g(u)$ is antisymmetric about $u=0$. Solutions of initial value problems tends to almost piecewise constant functions within $O(1)\e$ time. The almost constant pieces are separated by sharp interior layers, called fronts. The motion of these fronts are studied by asymptotic expansion. The equation for the motion of the front is obtained. In the case of $\bff=\bb u^2$ and $g(u)=au(1-u^2)$, where $\bb\in\RR^n$ and $0
- Paper:
- Available as PostScript (303 Kbytes) or gzipped PostScript (133 Kbytes; uncompress using gunzip).
- Author(s):
- Haitao Fan, <fan@math.georgetown.edu>
- Shi Jin, <jin@math.wisc.edu>
- Publishing information:
- Comments:
- Revised version, August 8 2001
- Submitted by:
- <fan@math.georgetown.edu> April 30 2001.
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