We consider travelling waves for a nonlinear diffusion equa tion with a bistable or multistable nonlinearity. The goal is to study how a plana r tr velling front interacts with a compact obstacle… (More)

We study the Cauchy problem ut = uxx + f (u) (t > 0, x ∈ R1), u(0, x) = u0(x) (x ∈ R1), where f (u) is a locally Lipschitz continuous function satisfying f (0) = 0. We show that any nonnegative… (More)

We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities – including multistable ones – and study the asymptotic behavior of solutions with… (More)

Formal asymptotic expansions have long been used to study the singularly perturbed Allen-Cahn type equations and reaction-diffusion systems, including in particular the FitzHugh-Nagumo system.… (More)

Abstract. We consider the Cauchy problem We consider the Cauchy problem ut = uxx + f(u), x ∈ R, t > 0, u(x, 0) = u0(x), x ∈ R, where f is a locally Lipschitz function on R with f(0) = 0, and u0 is a… (More)

We derive an upper bound for the radius R(t) of a vanishing bubble in a family of equivariant maps Ft : D2 → S2 which evolve by the harmonic map flow. The self-similar “type 1” radius would be R(t) =… (More)

An outbreak of nosocomial Campylobacter fetus meningitis occurred in a neonatal intensive care unit (NICU). Eight C. fetus strains were isolated from 4 infants with meningitis, the mother of the… (More)

We investigate the singular limit, as ε → 0, of the Allen-Cahn equation ut = ∆u ε + ε−2f(uε), with f a balanced bistable nonlinearity. We consider rather general initial data u0 that is independent… (More)

We study the following nonlinear Stefan problem ut − d∆u = g(u) for x ∈ Ω(t), t > 0, u = 0 and ut = μ|∇xu| for x ∈ Γ(t), t > 0, u(0, x) = u0(x) for x ∈ Ω0, where Ω(t) ⊂ R (n ≥ 2) is bounded by… (More)