Related papers: Correctors and error estimates for reaction-diffus…
In this paper we are concerned with convergence of solutions of the Poisson equation with Neumann boundary conditions in a two-dimensional thin domain exhibiting highly oscillatory behavior in part of its boundary. We deal with the resonant…
For a class of interacting particle systems in continuous space, we show that finite-volume approximations of the bulk diffusion matrix converge at an algebraic rate. The models we consider are reversible with respect to the Poisson…
We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a…
In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes…
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…
Coupled nonlinear system of reaction-diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct…
We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, and typical solutions oscillate with frequency proportional…
A steady-state convection-diffusion problem with a small diffusion of order $\mathcal{O}(\varepsilon)$ is considered in a thin three-dimensional graph-like junction consisting of thin cylinders connected through a domain (node) of diameter…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…
In this work, we construct a transformation between the solutions to the following reaction-convection-diffusion equation $$ \partial_t u=(u^m)_{xx}+a(x)(u^m)_x+b(x)u^m, $$ posed for $x\in\real$, $t\geq0$ and $m>1$, where $a$, $b$ are two…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
Let us consider the singularly perturbed model problem $Lu:=-\varepsilon\Delta u-bu_x+c u =f$ with homogeneous Dirichlet boundary conditions on $\Gamma=\partial\Omega$ $u|_\Gamma =0$ on the unit-square $\Omega=(0,1)^2$. Assuming that $b>0$…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
We study Hibridizable Discontinuous Galerkin (HDG) discretizations for a class of non-linear interior elliptic boundary value problems posed in curved domains where both the source term and the diffusion coefficient are non-linear. We…
We consider a semi-discrete finite element approximation for a system consisting of the evolution of a planar curve evolving by forced curve shortening flow inside a given bounded domain $\Omega \subset \mathbb{R}^2$, such that the curve…
We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in…
We present a full classification of the short-time behaviour of the interfaces and local solutions to the nonlinear parabolic $p$-Laplacian type reaction-diffusion equation of non-Newtonian elastic filtration \[…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…