Related papers: Spatially discrete reaction-diffusion equations wi…
Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one…
In this paper,under an abstract setting we establish the existence of spatially inhomogeneous steady states and the asymptotic propagation properties for a large class of monotone evolution systems without spatial translation invariance.…
We investigate the dynamics and morphology of jets propagating into the interstellar medium using 2D relativistic hydrodynamic simulations. The calculations are performed assuming axisymmetric geometry and trace a long propagation of jets.…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
We study analytically the dynamics and the micro-structural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active micro-rheology…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…
We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion i.e. we observe the…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise,…
We study a hybrid impulsive reaction-advection-diffusion model given by a reaction-advection-diffusion equation composed with a discrete-time map in space dimension $n\in\mathbb N$. The reaction-advection-diffusion equation takes the form…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
The dynamics of a point charged particle which is driven by a uniform external electric field and moves in a medium of elastic scatterers is investigated. Using rudimentary approaches, we reproduce, in one dimension, the known results that…
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction-diffusion equations in R N in any space dimension N. The solutions are assumed to be localized in the past. Under certain…
We consider a nonlinear Schroedinger equation in two spatial dimensions subject to a periodic honeycomb lattice potential. Using a multi-scale expansion together with rigorous error estimates, we derive an effective model of nonlinear Dirac…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…
In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…