In this short survey, we describe some recent developments on the modeling of propagation
by reaction-differential equations with free boundaries, which involve local as well as …

In this paper we investigate a diffusive logistic model with a free boundary in one space
dimension. We aim to use the dynamics of such a problem to describe the spreading of a …

This chapter contains a general presentation of parabolic partial differential equations that
are used in biology: Lotka-Volterra systems and chemical or enzymatic reactions. These are …

In this paper we investigate some free boundary problems for the Lotka–Volterra type prey–
predator model in one space dimension. The main objective is to understand the asymptotic …

We study the diffusive logistic equation with a free boundary in higher space dimensions
and heterogeneous environment. Such a model may be used to describe the spreading of a …

Abstract 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 …

In this paper we investigate a free boundary problem for the classical Lotka–Volterra type
predator–prey model with double free boundaries in one space dimension. This system …

In this paper we investigate two free boundary problems for a Lotka–Volterra type
competition model in one space dimension. The main objective is to understand the …

We consider Fisher-KPP equation with advection: ut= uxx− β u x+ f (u) for x∈(g (t), h (t)),
where g (t) and h (t) are two free boundaries satisfying Stefan conditions. This equation is …

This article is concerned with a system of semilinear parabolic equations with a free
boundary, which arises in a predator–prey ecological model. The conditions for the …