Generation and propagation of interfaces in reactiondiffusion systems
Author:
Xinfu Chen
Journal:
Trans. Amer. Math. Soc. 334 (1992), 877913
MSC:
Primary 35R35; Secondary 35K57
MathSciNet review:
1144013
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Abstract: This paper is concerned with the asymptotic behavior, as , of the solution of the second initialboundary value problem of the reactiondiffusion system: where is a constant. When , is bistable in the sense that the ordinary differential equation has two stable solutions and and one unstable solution , where , and are the three solutions of the algebraic equation . We show that, when the initial data of is in the interval , the solution of the system tends to a limit which is a solution of a free boundary problem, as long as the free boundary problem has a unique classical solution. The function is a "phase" function in the sense that it coincides with in one region and with in another region . The common boundary (free boundary or interface) of the two regions and moves with a normal velocity equal to , where is a function that can be calculated. The local (in time) existence of a unique classical solution to the free boundary problem is also established. Further we show that if initially takes both positive and negative values, then an interface will develop in a short time near the hypersurface where .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199211440133
PII:
S 00029947(1992)11440133
Keywords:
Reactiondiffusion systems,
generation of interface,
propagation of interface
Article copyright:
© Copyright 1992
American Mathematical Society
