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We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we…
In this paper, we provide a mathematical framework in studying the wave propagation with the annihilation phenomenon in excitable media. We deal with the existence and uniqueness of solutions to a one-dimensional free boundary problem…
In this paper, we study the Lotka-Volterra prey-predator models consisting of two species on finite connected graphs under Neumann condition and the condition that there is no boundary condition. We establish the global stability of the…
We investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of stochastic differential equations describing a prey-predator model perturbed by Gaussian noise. We first establish, for any fixed…
This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…
In this paper, we consider a Fisher-KPP equation with an advection term and two free boundaries, which models the behavior of an invasive species in one dimension space. When spreading happens (that is, the solution converges to a positive…
This paper continues the investigation of Du and Lou (J. European Math Soc, to appear), where the long-time behavior of positive solutions to a nonlinear diffusion equation of the form $u_t=u_{xx}+f(u)$ for $x$ over a varying interval…
We consider the diffusive Hamilton-Jacobi equation, with homogeneous Dirichlet conditions and regular initial data. It is known from [Barles-DaLio, 2004] that the problem admits a unique, continuous, global viscosity solution, which extends…
We study a parabolic free boundary problem, arising from a model for the propagation of equi-diffusional premixed flames with high activation energy. If an initial data is compactly supported, then the solution vanishes in a finite time,…
We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type…
This paper analyzes the generalized spatially heterogeneous diffusive predator-prey model introduced by the authors in \cite{LGMH20}, whose interaction terms depend on a saturation coefficient $m(x)\gneq0$. As the amplitude of the…
We present a spatial, individual-based predator-prey model in which dispersal is dependent on the local community. We determine species suitability to the biotic conditions of their local environment through a time and space varying fitness…
A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…
In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.
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…
Following the well-extablished mathematical approach to persistence and its recent developments we give a rigorous theoretical explanation to the numerical results obtained for a certain prey-predator model with functional response of…
The paper deals with a West Nile virus (WNv) model, where the nonlocal diffusion is introduced to characterize a long-range dispersal, the free boundary is used to describe the spreading front, and seasonal succession accounts for the…
We consider the initial-boundary value problem for an incompressible Oldroyd-B model with stress diffusion in two-dimensional upper half plane which describes the motion of viscoelastic polymeric fluids. From the physical point of view, the…
A discrete chemotactic predator-prey model is proposed in which the prey secrets a diffusing chemical which is sensed by the predator and vice versa. Two dynamical states corresponding to catching and escaping are identified and it is shown…
In this paper, we investigate the effect of dispersal and advection on the dynamics of a predator-prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the…