相关论文: Large-time asymptotics for degenerate cross-diffus…
Starting from a sequence of independent Wright-Fisher diffusion processes on $[0,1]$, we construct a class of reversible infinite dimensional diffusion processes on $\DD_\infty:= \{{\bf x}\in [0,1]^\N: \sum_{i\ge 1} x_i=1\}$ with GEM…
The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with…
We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy…
The nonlinear Forchheimer equations are used to describe the dynamics of fluid flows in porous media when Darcy's law is not applicable. In this article, we consider the generalized Forchheimer flows for slightly compressible fluids and…
Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in…
We prove existence of the largest entropy sub-solution and the smallest entropy super-solution to the Cauchy problem for a nonlinear degenerate parabolic equation with only continuous flux and diffusion functions. Applying this result, we…
We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical mechanics and population dynamics. These equations can be…
Here, we consider anisotropic degenerate parabolic-hyperbolic equations and degenerate quasilinear Hamilton-Jacobi equations. We prove the equivalence of two notions of entropy and viscosity solutions of two equations, and apply it to…
An initial boundary value problem of the nonlinear diffusion equation with a dynamic boundary condition is treated. The existence problem of the initial-boundary value problem is discussed. The main idea of the proof is an abstract approach…
We consider a scalar, possibly degenerate parabolic equation with a source term, in several space dimensions. For initial data with bounded variation we prove the existence of solutions to the initial-value problem. Then we show that these…
In this paper, we consider the infinite dimensional linear control system describing population models structured by age, size, and spatial position. The diffusion coefficient is degenerate at a point of the domain or both extreme points.…
We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective part of the…
We study diffusion processes that are stopped or reflected on the boundary of a domain. The generator of the process is assumed to contain two parts: the main part that degenerates on the boundary in a direction orthogonal to the boundary…
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…
We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of…
In this contribution we analyze the large time behavior of a family of nonlinear finite volume schemes for anisotropic convection-diffusion equations set in a bounded bidimensional domain and endowed with either Dirichlet and / or no-flux…
In this work, we introduce a cross-diffusion model that couples population density and occupied area to investigate how internal pressure drives growth and motility. By blending nonlinear nonlocal interactions with porous-medium diffusion…