Klemens Fellner

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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)
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)
In the continuation of [DF], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L ∞ bound via(More)
We study a scalar conservation law with a nonlinear dissipative inhomogeneity, which serves as a simplified model for nonlinear heat radiation effects in high–temperature gases. We establish global existence and uniqueness of weak entropy solutions along with L contraction and monotonicity properties of the solution semigroup. We derive explicit threshold(More)
The Aizenman-Bak model for reacting polymers is considered for spatially inhomogeneous situations in which they diffuse in space with a nondegenerate size-dependent coefficient. Both the break-up and the coalescence of polymers are taken into account with fragmentation and coagulation constant kernels. We demonstrate that the entropy-entropy dissipation(More)
In this paper, we are concerned with a class of multi-dimensional balance laws with a non-local dissipative source which arise as simplified models for the hydrodynamics of radiating gases. At first we introduce the energy method in the setting of smooth perturbations and study the stability of constants states. Precisely, we employ Fourier space analysis(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 apriori estimates and duality methods, we prove exponential convergence of these solutions towards equilibrium with explicit rates in all space dimensions.(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)