相关论文: Quenching phenomena in a system of non-local diffu…

In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection- diffusion type is considered on the interval [0, 1]. The components of the solution of this…

Interfacial phenomena associated with fluid adsorption in two dimensional systems has recently been shown to exhibit hidden symmetries, or covariances, which precisely relate local adsorption properties in different confining geometries. We…

In this paper, we study the asymptotic behavior of the solutions of nonlocal bistable reaction-diffusion equations starting from compactly supported initial conditions. Depending on the relationship between the nonlinearity, the interaction…

We consider networks of reaction-diffusion systems of Hodgkin-Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as existence of invariant regions and of the attractor. Then,…

In this article, we address the absorption properties of a class of stochastic differ- ential equations around singular points where both the drift and diffusion functions vanish. According to the H\"older coefficient alpha of the diffusion…

The famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…

Carrying out explicitly the computation in a paradigmatic model of non-interacting systems, the Gaussian Model, we show the existence of a singular point in the probability distribution $P(M)$ of an extensive variable $M$. Interpreting…

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy…

The general possible form of meanfield parameterization in a running frame in terms of current, energy and density functionals are examined under the restrictions of Galilean invariance. It is found that only two density-dependent…

We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion…

When $2N/(N+1)<p<2$ and $0<q<p/2$, non-negative solutions to the singular diffusion equation with gradient absorption $$\partial\_tu-\Delta\_p u + |\nabla u|^q=0 \ \text{ in }\ (0,\infty)\times\mathbb{R}^N$$ vanish after a finite time. This…

The pioneering work of Brezis-Merle [7], Li-Shafrir [27], Li [26] and Bartolucci-Tarantello [4] showed that any sequence of blow up solutions for (singular) mean field equations of Liouville type must exhibit a "mass concentration"…

We consider the subdiffusion--absorption process in a system which consists of two different media separated by a thin membrane. The process is described by subdiffusion--absorption equations with fractional Riemann--Liouville time…

We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite time the latter induces entanglement between right- and left- moving density…

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

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…

In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the…

The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…

We develop general heterogeneous nonlocal diffusion models and investigate their connection to local diffusion models by taking a singular limit of focusing kernels. We reveal the link between the two groups of diffusion equations which…

We study the large-time behaviour of the solutions $u$ of the evolution equation involving nonlinear diffusion and gradient absorption $\partial_t u - \Delta_p u + |\nabla u|^q=0$. We consider the problem posed for $x\in {\mathbb R}^N $ and…