相关论文: A Free Boundary Problem for a Ratio-dependent Pred…

The work presents the analysis of the free boundary value problem related to the invasion model of new species in biofilm reactors. In the framework of continuum approach to mathematical modelling of biofilm growth, the problem consists of…

We study the existence and multiplicity of solutions of the following free boundary problem $$ (P)\left\{ \begin{array}{rcll} \del u &=& \lam ( \eps +(1-\eps ) H(u-\mu))~ \hspace{3mm}&\text{in}~\Omega (t)\\ u&=&…

We construct exact solutions for a system of two nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the…

The goal of this work is to analyze a model for the rate-independent evolution of sets with finite perimeter. The evolution of the admissible sets is driven by that of a given time-dependent set, which has to include the admissible sets and…

In this work, we show how to obtain a free boundary problem as the limit of a fully non linear elliptic system of equations that models population segregation (Gause-Lotka-Volterra type). We study the regularity of the solutions. In…

We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one…

In this paper, we mainly study the propagation properties of a nonlocal dispersal predator-prey system in a shifting environment. It is known that Choi et al. [J. Differ. Equ. 302 (2021), pp. 807-853] studied the persistence or extinction…

We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the…

A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to a singular perturbation problem for a strongly degenerate parabolic partial differential equation in 1D. We present a conjecture for an asymptotic…

This paper focus on the diffusive eco-epidemiological prey-predator model with infectious diseases in prey, and with the homogeneous Neumann and Dirichlet boundary conditions, respectively. When boundary conditions are homogeneous Neumann…

We study a chemotaxis system that includes two competitive prey and one predator species in a two-dimensional domain, where the movement of prey (resp. predators) is driven by chemicals secreted by predators (resp. prey), called mutually…

We study a simple model of a diffusing particle (the prey) that on encounter with one of a swarm of diffusing predators can either perish or be reset to its original position at the origin. We show that the survival probability of the prey…

In ecology, prey switching refers to a predator's adaptive change of habitat or diet in response to prey abundance. In this paper, we study piecewise-smooth models of predator-prey interactions with a linear trade-off in a predator's prey…

We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of prey-predator system is apparent rather than real and there are still many of its hidden properties that have been…

The existence and uniqueness of a global positive solution is proven for the system of stochastic differential equations describing a nonautonomous stochastic density dependent predator-prey model with Holling-type II functional response…

A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary…

In models for the evolution of predation from initially purely competitive species interactions, the propensity of predation is most often assumed to be a direct consequence of the relative morphological and physiological traits of…

We study the transmission problem in bounded domains with dissipative boundary conditions. Under some natural assumptions, we prove uniform bounds of the corresponding resolvents on the real axis at high frequency, and as a consequence, we…

We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…

We propose and investigate a discrete-time predator-prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson-Bailey host-parasitoid system with density dependent growth rate. A…