相关论文: Travelling Waves in Monostable and Bistable Stocha…

The paper is devoted to a reaction-diffusion equation with delay arising in modelling the immune response. We prove the existence of travelling waves in the bistable case using the Leray-Schauder method. In difference with the previous…

The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{\"o}dinger (NLS) equation on periodic metric graphs can be reduced asymptotically on long…

In this paper we focus on a discrete physical model describing granular crystals, whose equations of motion can be described by a system of differential difference equations (DDEs). After revisiting earlier continuum approximations, we…

We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…

A framework to establish response theory for a class of nonlinear stochastic partial differential equations (SPDEs) is provided. More specifically, it is shown that for a certain class of observables, the averages of those observables…

We examine travelling wave solutions of the reaction-diffusion equation, $\partial_t u= R(u) + \partial_x \left[D(u) \partial_x u\right]$, with a Stefan-like condition at the edge of the moving front. With only a few assumptions on $R(u)$…

Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated…

New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.

We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We…

The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…

The Stochastic Partial Differential Equation (SPDE) approach, now commonly used in spatial statistics to construct Gaussian random fields, is revisited from a mechanistic perspective based on the movement of microscopic particles, thereby…

Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks…

We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…

Cortical spreading depression and spreading depolarization (CSD) are waves of neuronal depolarization that spread across the cortex, leading to a temporary saturation of brain activity. They are associated to various brain disorders such as…

In this paper we establish the meta-stability of travelling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the phase-tracking technique developed in…

We apply the method of simplest equation for obtaining exact solitary traveling-wave solutions of nonlinear partial differential equations that contain monomials of odd and even grade with respect to participating derivatives. We consider…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of…

We consider SDEs with (distributional) drift in negative Besov spaces and random initial condition and investigate them from two different viewpoints. In the first part we set up a martingale problem and show its well-posedness.We then…

We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We present our analytical results on the existence, uniqueness (up…