Related papers: Exact Solutions of Low-Dimensional Reaction-Diffus…
We consider a system of three reaction-diffusion equations modeling the interaction between a prey species and two predators species including functional responses of Holly type-II and Leslie-Gower type. We propose a reaction-diffusion…
While it is known that Hamiltonian systems may undergo a phenomenon of condensation akin to Bose-Einstein condensation, not all the manifestations of this phenomenon have been uncovered yet. In this work we present a novel form of…
We analyze the two-species reaction-diffusion system including trapping reaction $A + B \to A$ as well as coagulation/annihilation reactions $A + A \to (A,0)$ where particles of both species are performing L\'evy flights with control…
This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one…
The exact solution of a diffusion$-$reaction model for the trapping and annihilation of positrons in small extended spherical defects (clusters, voids, small precipitates) with competitive rate-limited trapping in vacancy-type point defects…
Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…
The aim of this paper is to study a class of positive solutions of the fast diffusion equation with specific persistent singular behavior. First, we construct new types of solutions with anisotropic singularities. Depending on parameters,…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
We present an approach based on entropy and duality methods for triangular reaction cross diffusion systems of two equations, in which cross diffusion terms appear only in one of the equations. Thanks to this approach, we recover and extend…
Q-conditional (nonclassical) symmetries of the known three-component reaction-diffusion system [K. Aoki et al Theor. Pop. Biol. 50(1) (1996)] modeling interaction between farmers and hunter-gatherers are constructed for the first time. A…
We present in this work a very short proof for the existence, uniqueness and smoothness in dimensions $d\leq 3$ of the system of reaction diffusion $ \partial\_t a\_i - d\_i \Delta a\_i = (-1)^i (a\_1 a\_3 - a\_2 a\_4)$, where $a\_i \geq 0$…
This paper investigates a reaction-advection-diffusion system modeling interspecific competition between two species over bounded domains. The kinetic terms are assumed to satisfy the Beddington-DeAngelis functional responses. We consider…
This paper is devoted to the multigrid convergence analysis for the linear systems arising from the conforming linear finite element discretization of the second order elliptic equations with anisotropic diffusion. The multigrid convergence…
A system of a parabolic partial differential equation coupled with ordinary differential inclusions that arises from a closed-loop control problem for a thermodynamic process governed by the Allen-Cahn diffusion reaction model is studied. A…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
We provide the proof of convergence of the directional diffusion splitting scheme for two-dimensional parabolic and elliptic advection-diffusion-reaction problems with certain restrictions on problem data
In this paper we consider the mathematical relationship between nonlocal interactions of convolution type and multiple diffusive substances in high dimensions. Motivated by that the nonlocal evolution equations reproduce similar patterns to…
In this paper we consider a simple two patch reaction diffusion model with strong Allee effect, sufficiently distinct carrying capacities, similar reaction strengths, and strong diffusion. In the homogeneous case, i.e., in in the case of…
We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…
This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the…