Free Boundary Problems for a Lotka–Volterra Competition System

A hybrid method for singularly perturbed delay boundary value problems exhibiting a right boundary layer

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

On Free Boundary Problems

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...

On a Free Boundary Problem for a Two-Species Weak Competition System

We study a Lotka–Volterra type weak competition model with a free boundary in a one-dimensional habitat. The main objective is to understand the asymptotic behavior of two competing species spreading via a free boundary. We also provide some sufficient conditions for spreading success and spreading failure, respectively. Finally, when spreading successfully, we provide an estimate to show that ...

An Existence Result for a Class of Free Boundary Problems an Existence Result for a Class of Free Boundary Problems

In this paper we study the existence of C 2;; domain solutions for a class of free boundary problems which are critical domains for a shape functional depending on a general term (in most PDE applications this term represents the energy associated) and the perimeter, under the constraint that the measure of is given. As an application there are considered two problems. They involve respectively...