Related papers: Fronts in reactive convection: bounds, stability a…
We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical…
The renormalization ideas of self-similar dynamics of a strongly turbulent flame front are applied to the case of a flame with realistically large thermal expansion of the burning matter. In that case a flame front is corrugated both by…
We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum of the linearised operator in full generality and identify…
The stability of density-stratified viscous Taylor-Couette flows is considered using the Boussinesq approximation but without any use of the short-wave approximation. The flows which are unstable after the Rayleigh criterion (\hat \mu<\hat…
It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of weak anisotropy by directional advection on such solutions, and…
The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar crack…
We study the velocity of travelling waves of a reaction-diffusion system coupling a standard reaction-diffusion equation in a strip with a one-dimensional diffusion equation on a line. We show that it grows like the square root of the…
Using the time-dependent Ginzburg-Landau equations we study the propagation of planar fronts in superconductors, which would appear after a quench to zero applied magnetic field. Our numerical solutions show that the fronts propagate at a…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…
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…
It has been argued that there is biological and modeling evidence that a non-linear diffusion coefficient of the type D(b) = D_0 b^{k} underlies the formation of a number of growth patterns of bacterial colonies. We study a…
The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…
We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system…
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
Second initial boundary problem in narrow domains of width $\epsilon\ll 1$ for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilistic methods we show that the solution…
In this paper we study the local instability to the boundary equilibria and the local stability to the positive equilibria for some chemical reaction-diffusion systems. We first analyze a three-species system with boundary equilibria in…
This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case a reaction-diffusion equation in a periodic medium with…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…