相关论文: Convergence to pulsating traveling waves with mini…

Sufficient conditions for either existence or non-existence of traveling wave solutions for a general quasi-linear reaction-diffusion-convection equation, possibly highly degenerate or singular, with discontinuous coefficients are…

Non-cooperative Fisher-KPP systems with space-time periodic coefficients are motivated for instance by models for structured populations evolving in periodic environments. This paper is concerned with entire solutions describing the…

We consider the one-dimensional KPP-equation driven by space-time white noise and extend the construction of travelling wave solutions arising from Heavyside initial data from [Tribe, 1996, MR1396765] to non-negative continuous functions…

The goal of this paper is to find the homogenized equation of a heterogenous Fisher-KPP model in a periodic medium. The solutions of this model are pulsating travelling fronts whose \emph{speeds} are superior to a parametric minimal speed…

The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of…

Some classes of the so called "travelling wave" solutions of Einstein and Einstein - Maxwell equations in General Relativity and of dynamical equations for massless bosonic fields in string gravity in four and higher dimensions are…

We study a Fisher-KPP equation with spatially periodic diffusion and reaction terms. We identify a class of periodic media for which the equation admits an explicit, closed-form solution. Through a nonlinear change of variables, the problem…

We consider the Fisher-KPP reaction-diffusion equation in the whole space. We prove that if a solution has, to main order and for all times (positive and negative), the same exponential decay as a planar traveling wave with speed larger…

We consider reaction-diffusion equations of porous medium type, with different kind of reaction terms, and nonnegative bounded initial data. For all the reaction terms under consideration there are initial data for which the solution…

This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us…

The current paper is devoted to the investigation of wave propagation phenomenon in reaction-diffusion equations with ignition type nonlinearity in time heterogeneous and random media. It is proven that such equations in time heterogeneous…

This paper concerns the existence and properties of traveling wave solutions to reaction-diffusion-convection equations on the real line. We consider a general diffusion term involving the $p$-Laplacian and combustion-type reaction term. We…

We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We…

In this study, we investigate a porous medium-type flux limited reaction--diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized…

We consider a Fisher-KPP-type equation, where both diffusion and nonlinear part are nonlocal, with anisotropic probability kernels. Under minimal conditions on the coefficients, we prove existence, uniqueness, and uniform space-time…

This paper is devoted to existence and non-existence results for generalized tran-sition waves solutions of space-time heterogeneous Fisher-KPP equations. When the coefficients of the equation are periodic in space but otherwise depend in a…

Spatially periodic reaction-diffusion equations typically admit pulsating waves which describe the transition from one steady state to another. Due to the heterogeneity, in general such an equation is not invariant by rotation and therefore…

We propose a novel method for establishing the convergence rates of solutions to reaction-diffusion equations to traveling waves. The analysis is based on the study of the traveling wave shape defect function introduced in [2]. It turns out…

This paper is concerned with a model for the dynamics of a single species in a one-dimensional heterogeneous environment. The environment consists of two kinds of patches, which are periodically alternately arranged along the spatial axis.…

This paper deals with front propagation dynamics of monostable equations with nonlocal dispersal in spatially periodic habitats. In the authors' earlier works, it is shown that a general spatially periodic monostable equation with nonlocal…