Related papers: Free boundary problems with nonlocal and local dif…
Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among $m$ ecological species for a limited resource necessary to…
We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this…
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled…
Motivated by a nonlocal free boundary problem, we study uniform properties of solutions to a singular perturbation problem for a boundary-reaction-diffusion equation, where the reaction term is of combustion type. This boundary problem is…
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…
This review summarizes all known results (up to this date) about methods of integration of the classical Lotka-Volterra systems with diffusion and presents a wide range of exact solutions, which are the most important from applicability…
In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [12] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to…
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 the convenience of a nonlocal dispersal strategy in a reaction-diffusion system with a fractional Laplacian operator. We show that there are circumstances - namely, a precise condition on the distribution of the resource - under…
This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the…
We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
We study existence and uniqueness of travelling fronts, and asymptotic speed of propagation for a non local reaction diffusion equation with spatial and genetic trait structure.
The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…
This paper studies the spreading dynamics of a high-dimensional strong competition Lotka-Volterra system where two species initially occupy disjoint measurable (possibly unbounded) subsets in $\mathbb{R}^N$, which are called initial…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…
We study the propagation speed of bistable traveling waves in the classical two-component diffusive Lotka-Volterra system under strong competition. From an ecological perspective, the sign of the propagation speed determines the long-term…
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 \[…
In this paper we study the following one-dimensional reaction-diffusion problem $$ u_t+(-\Delta)^s u=f(x-c t, u) \;\:\textrm{ in } \mathbb{R}\times (0,+\infty), $$ where $s>\frac{1}{2}$, $c \in \mathbb{R}$ is a prescribed velocity, and $f$…