Stability of travelling-wave solutions for reaction-diffusion-convection systems
| dc.creator | Crooks, E. C. M. | |
| dc.date | 2000-12-19 | |
| dc.date.accessioned | 2026-07-07T04:39:18Z | |
| dc.date.available | 2026-07-07T04:39:18Z | |
| dc.description | We 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.description | 23 pages. To appear in Topological Methods in Nonlinear Analysis | |
| dc.identifier | https://arxiv.org/abs/math/0012181 | |
| dc.identifier | http://arxiv.org/abs/math/0012181 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60606 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K45, 35K40, 35K55, 35B35, 35B40 | |
| dc.title | Stability of travelling-wave solutions for reaction-diffusion-convection systems | |
| dc.type | text |