Related papers: Reaction-diffusion models for a class of infinite-…
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 transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…
A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion-reaction problem with a reaction parameter tending…
In this paper, we explore the solvability and the optimal control problem for a compartmental model based on reaction-diffusion partial differential equations describing a transmissible disease. The nonlinear model takes into account the…
We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations…
In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.
The paper treats a reaction-diffusion equation with hysteretic nonlinearity on a one-dimensional lattice. It arises as a result of the spatial discretization of the corresponding continuous model with so-called nontransverse initial data…
This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such…
We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and to have locally Lipschitz nonlinearities of at most (slightly…
The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…
In this paper, we study the mixed problem for new class of nonlinear reaction-diffusion PDEs with the nonlocal nonlinearity with variable exponents. Here we obtain results on solvability and behavior of solutions both when these are yet…
The goal of this work is to establish the global existence of nonnegative classical solutions in all dimensions for a system of highly nonlinear reaction-diffusion equations. We address the case for different diffusion coefficients and the…
The paper studies the existence of solutions for the reaction-diffusion equation in $\mathbb R^2$ with point-interaction laplacian $\Delta_\alpha$ with $\alpha\in(-\infty,+\infty]$, assuming the functions to remain on the absolute…
In this paper we deal with a reaction-diffusion equation in a bounded interval of the real line with a nonlinear diffusion of Perona-Malik's type and a balanced bistable reaction term. Under very general assumptions, we study the…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…