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- Klemens Fellner, Gaël Raoul
- Mathematical and Computer Modelling
- 2011

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)

- Christian Schmeiser, Klemens Fellner
- SIAM Journal of Applied Mathematics
- 2004

- Emily J Hackett-Jones, Kerry A Landman, Klemens Fellner
- Physical review. E, Statistical, nonlinear, and…
- 2012

Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has both attractive and repulsive singularities. Currently, no existence theory for such potentials is available.… (More)

- Klemens Fellner, Lukas Neumann, Christian S hmeiser
- 2003

- 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)

- Laurent Desvillettes, Klemens Fellner
- SIAM J. Math. Analysis
- 2009

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 study convergence to equilibrium for certain spatially inhomoge-nous kinetic equations, such as discrete velocity models or a lineariza-tion of a kinetic model for cometary flow. For such equations, the convergence to a unique equilibrium state is the result of, firstly, the dissipative effects of the collision operator, which morphs the solution towards… (More)

- Klemens Fellner, Evangelos Latos, Giovanni Pisante
- Appl. Math. Lett.
- 2015

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)