Stability of travelling-wave solutions for reaction-diffusion-convection systems

dc.creatorCrooks, E. C. M.
dc.date2000-12-19
dc.date.accessioned2026-07-07T04:39:18Z
dc.date.available2026-07-07T04:39:18Z
dc.descriptionWe are concerned with the asymptotic behaviour of classical solutions of systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is a 'bistable' nonlinearity satisfying conditions which guarantee the existence of a comparison principle. Suppose that there is a travelling-front solution w with velocity c, that connects two stable equilibria of f. We show that if U is bounded, uniformly continuously differentiable and such that w(x) - U(x) is small when the modulus of x is large, then there exists y in R such that u(., t) converges to w(.+y-ct) in the C1 norm at an exponential rate as t tends to infinity. Our approach extends an idea developed by Roquejoffre, Terman and Volpert in the convectionless case, where f is independent of u_x.
dc.description23 pages. To appear in Topological Methods in Nonlinear Analysis
dc.identifierhttps://arxiv.org/abs/math/0012181
dc.identifierhttp://arxiv.org/abs/math/0012181
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60606
dc.subjectAnalysis of PDEs
dc.subject35K45, 35K40, 35K55, 35B35, 35B40
dc.titleStability of travelling-wave solutions for reaction-diffusion-convection systems
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