A class of cross diffusion parabolic systems given on bounded domains of IR, with arbitrary n, is investigated. We show that there is a global attractor with finite Hausdorff dimension which attracts all solutions. The result will be applied to the generalized Shigesada, Kawasaki and Teramoto (SKT) model with Lotka-Volterra reactions. In addition, the persistence property of the SKT model will ...

Evolution equations associated with irreversible physical processes like diffusion and heat conduction lead to parabolic partial differential equations. When the equation is a model for a reversible physical process like propagation of acoustic or electromagnetic waves, then the evolution equation is generally hyperbolic. The mathematical models usually begin with a conservation statement that ...

We derive stochastic equations to describe reflected diffusion processes associated with the Cauchy-Neumann problem for systems of nonlinear parabolic in non-divergent form half-space. As a result, we obtain probabilistic representations weak solutions this problem.

The kinetics of K exchange were investigated in Ca-saturated samples from the Ap horizon of an Evesboro soil from Delaware. Biphasic kinetics characterized the first-order plots for K adsorption and desorption at 283 and 298K with the two simultaneous reactions being attributed to exchange sites with varying reactivity for K and Ca ions. The rapid reaction was ascribed to exchange sites of the ...

We study the global existence of parabolic-parabolic Keller–Segel system in Rd, d≥2. prove that initial data arbitrary size give rise to solutions provided diffusion parameter τ is large enough equation for chemoattractant. This fact was observed before two-dimensional case by Biler et al. (2015) [7] and Corrias (2014) [12]. Our analysis improves earlier results extends them any dimension d≥3. ...

We investigate degenerate cross-diffusion equations, with a rank-deficient diffusion-matrix, modelling multispecies population dynamics driven by partial pressure gradients. These equations have recently been found to arise in mean-field limit of interacting stochastic particle systems. To date, their analysis multiple space dimensions has confined the purely convective case equal mobility coef...

We derive the hydrodynamic limit of a kinetic equation with stochastic, short range perturbation velocity operator. Under some mixing hypotheses on stochastic perturbation, we establish diffusion-approximation result: obtain is parabolic partial differential macroscopic parameter, density here.

Abstract We consider the singular limit problem for Cauchy of (Patlak–) Keller–Segel system parabolic-parabolic type. The is considered in uniformly local Lebesgue spaces and as relaxation parameter $$\tau $$ τ goes to infinity, solution equation converges a drift-diffusion strong topology. For proof, we foll...