Preprint 2001-015

Front Motion in Muti-dimensional conservation Laws with Stiff Source Terms Driven by Mean Curvature and Variation of Front Thickness

Haitao Fan and Shi Jin


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.


[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <conservation@math.ntnu.no>
Last modified: Wed Aug 8 09:21:57 MET DST 2001