Related papers: Freezing Stochastic Travelling Waves
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of…
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…
We extend the result on the stability of travelling waves for stochastic Nagumo equations in [St] to general bistable reaction-diffusion equations with both additive and multiplicative noise, using a variational approach based on functional…
Many physical, chemical and biological systems have an inherent discrete spatial structure that strongly influences their dynamical behaviour. Similar remarks apply to internal or external noise, as well as to nonlocal coupling. In this…
The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…
We investigate the stability of traveling-pulse solutions to the stochastic FitzHughNagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framework can incorporate versions of the stochastic neural field…
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in $L^2$-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
In this paper we investigate the implementation of the so-called freezing method for second order wave equations in one and several space dimensions. The method converts the given PDE into a partial differential algebraic equation which is…
In this paper we consider the stochastic primitive equation for geophysical flows subject to transport noise and turbulent pressure. Admitting very rough noise terms, the global existence and uniqueness of solutions to this stochastic…
We consider synchronization by noise for stochastic partial differential equations which support traveling pulse solutions, such as the FitzHugh-Nagumo equation. We show that any two pulse-like solutions which start from different positions…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
This article considers the variational wave equation with viscosity and transport noise as a system of three coupled nonlinear stochastic partial differential equations. We prove pathwise global existence, uniqueness, and temporal…
We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of $N$ evolving particles which can be described by a noisy traveling wave equation with a noise of order $N^{-1/2}$. Our model can be viewed as the…
In this article, we construct a Stratonovich solution for the stochastic wave equation in spatial dimension $d \leq 2$, with time-independent noise and linear term $\sigma(u)=u$ multiplying the noise. The noise is spatially homogeneous and…
This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…