Related papers: Velocity Selection for Propagating Fronts in Super…
We study the three-dimensional Ginzburg-Landau model of superconductivity for strong applied magnetic fields varying between the second and third critical fields. In this regime, it is known from physics that superconductivity should be…
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both…
We consider flame front propagation in channel geometries. The steady state solution in this problem is space dependent, and therefore the linear stability analysis is described by a partial integro-differential equation with a space…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…
We study the features of the superconductivity nucleation and vortex configurations in superconductors with modulated disorder. Using the Ginzburg-Landau-type theory with spatially varying diffusion coefficient, we uncover and explain the…
We obtain a criterion for pulsating front speed-up by general periodic incompressible flows in two dimensions and in the presence of KPP nonlinearities. We achieve this by showing that the ratio of the minimal front speed and the effective…
We study the vortex formation in extreme type-II superconductors immersed in strong magnetic fields in the framework of the the Ginzburg-Landau theory. We focus on the regime where superconductivity survives in the bulk of the material but…
We study evolution of pulses propagating through focusing nonlinear media. Small disturbance on the smooth initial non-uniform background leads to formation of the region of strong nonlinear oscillations. We develop here an asymptotic…
We consider bistable reaction-diffusion equations in funnel-shaped domains of R N made up of straight parts and conical parts with positive opening angles. We study the large time dynamics of entire solutions emanating from a planar front…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
We study the 2D Ginzburg-Landau theory for a type-II superconductor in an applied magnetic field varying between the second and third critical value. In this regime the order parameter minimizing the GL energy is concentrated along the…
We study a generalized Ginzburg-Landau equation that models a sample formed of a superconducting/normal junction and which is not submitted to an applied magnetic field. We prove the existence of a unique positive (and bounded) solution of…
Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg - Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the "distance" to the…
We consider the damped hyperbolic equation in one space dimension $\epsilon u_{tt} + u_t = u_{xx} + F(u)$, where $\epsilon$ is a positive, not necessarily small parameter. We assume that $F(0)=F(1)=0$ and that $F$ is concave on the interval…
We study the asymptotic speed of traveling fronts of the scalar reaction diffusion for positive reaction terms and with a diffusion coefficient depending nonlinearly on the concentration and on its gradient. We restrict our study to…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
The problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms…
We consider reaction-diffusion equations with combustion-type non-linearities in two dimensions and study speed-up of their pulsating fronts by general periodic incompressible flows with a cellular structure. We show that the occurence of…
We study the localized stationary solutions of the one-dimensional time-dependent Ginzburg-Landau equations in the presence of a current. These threshold perturbations separate undercritical perturbations which return to the normal phase…
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…