Related papers: From non-local to classical SKT systems: triangula…
We prove that, under a suitable rescaling of the integrable kernel defining the nonlocal diffusion terms, the corresponding sequence of solutions of the Shigesada-Kawasaki-Teramoto nonlocal cross-diffusion problem converges to a solution of…
The global-in-time existence of renormalized solutions to reaction-cross-diffu-sion systems for an arbitrary number of variables in bounded domains with no-flux boundary conditions is proved. The cross-diffusion part describes the…
The existence of global weak solutions to the cross-diffusion model of Shigesada, Kawasaki, and Teramoto for an arbitrary number of species is proved. The model consists of strongly coupled parabolic equations for the population densities…
We consider some cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. We establish the global existence of strong solutions to…
In this paper we analyse a finite volume scheme for a nonlocal version of the Shigesada-Kawazaki-Teramoto (SKT) cross-diffusion system. We prove the existence of solutions to the scheme, derive qualitative properties of the solutions and…
We establish the uniqueness and regularity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in…
A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…
The convergence to equilibrium of renormalized solutions to reaction-cross-diffusion systems in a bounded domain under no-flux boundary conditions is studied. The reactions model complex balanced chemical reaction networks coming from…
We present new results of existence of global solutions for a class of reaction cross-diffusion systems of two equations presenting a cross-diffusion term in the first equation, and possibly presenting a self-diffusion term in any (or both)…
We establish the positivity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population…
For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smooth solution given by Amann theorem is actually global. This…
In a previous paper(2021), the author studied the asymptotic behavior of coexistence steady-states to the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. As a result, he proved that…
In this contribution we obtain partial $C^{0,\alpha}$-regularity for bounded solutions of a certain class of cross-diffusion systems, which are strongly coupled, degenerate quasilinear parabolic systems. Under slightly more restrictive…
We prove the existence and uniqueness of solution of a nonlocal cross-diffusion competitive population model for two species. The model may be considered as a version, or even an approximation, of the paradigmatic…
Population cross-diffusion systems of Shigesada-Kawasaki-Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion…
This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…
For cross-diffusion systems possessing an entropy (i.e. a Lyapunov functional)we study nonlocal versions and exhibit sufficient conditions to ensure that thenonlocal version inherits the entropy structure. These nonlocal systems can…
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…
An implicit Euler finite-volume scheme for an $n$-species population cross-diffusion system of Shigesada--Kawasaki--Teramoto-type in a bounded domain with no-flux boundary conditions is proposed and analyzed. The scheme preserves the formal…
We establish the existence of strong solutions to a class of cross diffusion systems on $\RR^N$ consists of $m$ equations ($m,N\ge 2$). which generalizes the Shigesada-Kawasaki-Teramoto (SKT) model in population dynamics. We introduce the…