The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator–prey reaction–diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state ...

Abstract We consider a degenerate scalar parabolic equation, in one spatial dimension, of flux-saturated type. The equation also contains convective term. study the existence and regularity traveling-wave solutions; particular we show that they can be discontinuous. Uniqueness is recovered by requiring an entropy condition, entropic solutions turn out to vanishing-diffusion limits with addition...

Photothermal diffusion-wave imaging is a promising technique for the analysis of a range of media. However, traditional diffusion-wave techniques are limited by the physics of parabolic diffusion and can only produce depth-integrated planar images. Here, we report a depth-resolved photothermal imaging modality, henceforth termed truncated-correlation photothermal coherence tomography (TC-PCT). ...

A strongly coupled cooperative parabolic system, which describes fecally-orally epidemic model with cross-diffusion in a heterogeneous environment, was formulated and analyzed. The basic reproduction number R0 , which serves as a threshold parameter that predicts whether the coexistence will exist or not, is introduced by the next infection operator and the related eigenvalue problems. By apply...

Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model [10]. The implications of nonlinear diffusion are that solutions exist globally and are uniformly bounded in time. We analyse the stationary case showing the existence of a unique, up to translation, global minimizer of the associa...

We consider the development of Implicit-Explicit (IMEX) RungeKutta schemes for hyperbolic and kinetic equations in the diffusion limit. In such regime the system relaxes towards a parabolic diffusion equation and it is desirable to have a method that is able to capture the asymptotic behavior with an implicit treatment of limiting diffusive terms. To this goal we reformulate the problem by prop...

The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first-passage time (MFPT) as a function of the potential parameters, the noise intensity and the mean rate of switch...

This work is devoted to examining the uniqueness and existence of kinetic solutions for a class scalar conservation laws involving nonlocal super-critical diffusion operator multiplicative noise. Our proof based upon analysis on double variables method enabled by parabolic approximation.

In addition, we suppose that sufficient compatibility conditions among the data of the differential equation hold, in order that the exact solution ~u ∈ C4,3(Q̄), i.e, continuity up to fourth order in space and up to third order in time. This problem is a simple model of the classical linear double–diffusion model for saturated flow in fractured porous media (Barenblatt system) developed in [1]....

The paper studied the processes represented by a system of equations particular product parabolic type. For solution mutual diffusion problems, evaluations were obtained according to environmental parameters and dimensions space. Computational schemes, algorithms, software packages in programming environments developed, solutions visualized solve problems.