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Stability of a front for a nonlocal conservation law

Published online by Cambridge University Press:  14 November 2011

Amine Asselah
Amine Asselah
Affiliation:
Department of Mathematics, Rutgers University, Hill Center, Busch Campus, New Brunswick NJ 08903, U.S.A.
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Abstract

We study the stability of a front for the law 2wt − (wx − γ(1 − w2)(K * w)x)x = 0. It was proved by Del Passo and De Mottoni that an increasing stationary solution, u, exists. We show that it is stable in the following sense: there is ε > 0 such that if w(0) = u + v with |v|2 < ε, then there is α(t) differentiable such that w(x, t) = u(α(t) + x) + v(x, t) and supℝ |v(x, t)| converges to 0 as t goes to infinity. Also, if v is initially odd, α(t) ≡ 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 2 , 1998 , pp. 219 - 234
Copyright
Copyright © Royal Society of Edinburgh 1998

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References

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