相关论文: Wavefront Solutions for Reaction-diffusion-convect…

We consider a diffusion and a wave equations: $$ \partial_t^ku(x,t) = \Delta u(x,t) + \mu(t)f(x), \quad x\in \Omega, \, t>0, \quad k=1,2 $$ with the zero initial and boundary conditions, where $\Omega \subset \mathbb{R}^d$ is a bounded…

In this paper, we study a tensor-based method for the numerical solution of a class of diffusion--reaction equations defined on spatial domains that admit common curvilinear coordinate representations. Typical examples in 2D include disks…

The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…

We propose a system of two coupled parabolic equations that have degenerate diffusion constants depending on the energy-like variable. The dissipation of the velocity-like variable is fed as a source term into the energy equation leading to…

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…

This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that each bounded positive solution of the convolution equation…

We prove existence and uniqueness of \emph{eternal solutions} in self-similar form growing up in time with exponential rate for the weighted reaction-diffusion equation $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, $$ posed in $\real^N$, with…

In this paper existence and nonexistence results of positive radial solutions of a Dirichlet $m$-Laplacian problem with different weights and a diffusion term inside the divergence of the form $\big(a(|x|)+g(u)\big)^{-\gamma}$, with…

We solve the convection-diffusion equation using a coupling of cell-centered finite volume (FV) and discontinuous Galerkin (DG) methods. The domain is divided into disjoint regions assigned to FV or DG, and the two methods are coupled…

For a fixed bounded domain $D \subset \mathbb{R}^N$ we investigate the asymptotic behaviour for large times of solutions to the $p$-Laplacian diffusion equation posed in a tubular domain \begin{equation*} \partial_t u = \Delta_p u \quad…

This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving…

In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…

We consider a singular parabolic equation of form \[ u_t = u_{xx} + \frac{\alpha}{2}(\mathrm{sgn}\,u_x)_x \] with periodic boundary conditions. Solutions to this kind of equations exhibit competition between smoothing due to one-dimensional…

In this paper, we define the transition semi-wave solution of the following reaction diffusion equation with free boundaries \begin{equation}\label{0.1} \left\{ \begin{aligned} u_{t}=u_{xx}+f(t,x,u),\ \ &t\in\Real, x<h(t), u(t,h(t))=0,\ \…

We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this equation was derived from a model of active Brownian particles…

This paper focuses on traveling wave solutions for the so-called Rosenzweig-MacArthur model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic…

A semi-Lagrangian method for parabolic problems is proposed, that extends previous work by the authors to achieve a fully conservative, flux-form discretization of linear and nonlinear diffusion equations. A basic consistency and…

Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…

In this paper we present a fast algorithm for the numerical solution of systems of reaction-diffusion equations, $\partial_t u + a \cdot \nabla u = \Delta u + F (x, t, u)$, $x \in \Omega \subset \mathbf{R}^3$, $t > 0$. Here, $u$ is a…

In this work, we consider an extension to parabolic problems of the variational multiscale method with spectral approximation of the sub-scales. We first discretize in time using a finite difference scheme and second, apply the…