Effects of small spatial variation of the reproduction rate in a two species competition model.
Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions
Enhancement of the traveling front speeds in reaction-diffusion equations with advection
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds.
Entropy solution for anisotropic reaction-diffusion-advection systems with L1 data.
In this paper, we study the question of existence and uniqueness of entropy solutions for a system of nonlinear partial differential equations with general anisotropic diffusivity and transport effects, supplemented with no-flux boundary conditions, modeling the spread of an epidemic disease through a heterogeneous habitat.
Equivalence and new exact solutions to the Black Scholes and diffusion equations.
Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the...
Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present....
Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems
The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the and error estimates are established. At the end...
Estimates for the norms of solutions of delay difference systems.
Estimates for the norms of solutions of difference systems with several delays.
Étude de l'existence de solutions globales d'un système de réaction-diffusion parabolique fortement non linéaire
Evolutionary Games in Space
The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop...
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
Exact linear lumping in abstract spaces.
Existence and Asymptotic Behaviour of Solutions in a System of Reaction Diffusion Equations.
Existence and attractors of solutions for nonlinear parabolic systems.
Existence and global exponential stability of equilibrium solution to reaction-diffusion recurrent neural networks on time scales.
Existence and non-existence results for a nonlinear heat equation.