We consider an Allen-Cahn type equation of the form ut = âˆ†u + Îµf(x, t, u), where Îµ is a small parameter and f(x, t, u) = f(u) âˆ’ Îµg(x, t, u) a bistable nonlinearity associated with a double-wellâ€¦ (More)

In this note, we give a positive answer to a question addressed in Nadin et al. (2011) [7]. To be precise, we prove that, for any kernel and any slope at the origin, there exist traveling waveâ€¦ (More)

In this paper we deal with polynomials orthogonal with respect to an inner product involving derivatives, that is, a Sobolev inner product. Indeed, we consider Sobolev type polynomials which areâ€¦ (More)

We consider a class of nonlocal reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. By using explicit changes of unknown function, we show that they areâ€¦ (More)

We consider a model of cellular detonations in gases. They consist in conservation laws with a non-local pseudo-differential operator whose symbol is asymptotically |Î¾|Î», where 0 < Î» â‰¤ 2; it can beâ€¦ (More)

We consider the homogeneous integro-differential equation âˆ‚tu = J âˆ—uâˆ’u+f(u) with a monostable nonlinearity f . Our interest is twofold: we investigate the existence/non existence of travelling waves,â€¦ (More)

We consider the mass conserving Allen-Cahn equation proposed in [8]: the Lagrange multiplier which ensures the conservation of the mass contains not only nonlocal but also local effects (in contrastâ€¦ (More)