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We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin. For locally attractive singular interaction… (More)

In the continuation of [DF], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) in two situations of degeneracy: Firstly, for a two species system, we show explicit exponential convergence to the unique constant steady state when spatial diffusion of one specie vanishes but the system still obeys the… (More)

- J. A. Cañizo, K. Fellner
- 2009

We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L 2 bound on the mass density and was previously used, for instance, in the context… (More)

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose… (More)

We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow up of solutions subject to sufficiently large initial data provided that the reaction term " overpowers " the nonlinear diffusion in a certain… (More)

- K. Fellner V. Kovtunenko, KLEMENS FELLNER, VICTOR A. KOVTUNENKO
- 2014

A nonlinear Poisson–Boltzmann equation with transmission boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic multiphase medium with dilute solid particles. The key issue is that the interfacial transfer allows jumps and thus… (More)

We consider a prototypical nonlinear reaction-diffusion system arising in reversible chemistry. Based on recent existence results of global weak and classical solutions derived from entropy-decay related a-priori estimates and duality methods, we prove exponential convergence of these solutions towards equilibrium with explicit rates in all space… (More)

11:20am-12:10pm Stability of rarefaction waves to the 1D compressible Navier-Stokes equations with density-dependent viscosity 02:00pm-02:50pm Some recent mathematical contributions to multiscale modelling for polymeric fluids Tony Lelievre, École Nationale Des Ponts Et Chaussées, France 02:50pm-03:40pm A seamless multiscale method and its application to… (More)