8 papers · 1 filter
Global renormalised solutions and equilibration of reaction-diffusion systems with non-linear diffusion
Klemens Fellner, Julian Fischer, Michael Kniely +1
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to ha…
Uniform-in-time bounds for quadratic reaction-diffusion systems with mass dissipation in higher dimensions
Klemens Fellner, Jeff Morgan, Bao Quoc Tang
Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and t…
Weak differentiability of the control-to-state mapping in a parabolic equation with hysteresis
Martin Brokate, Klemens Fellner, Matthias Lang-Batsching
We consider the heat equation on a bounded domain subject to an inhomogeneous forcing in terms of a rate-independent (hysteresis) operator and a control variable. The aim of the pa…
Large-time asymptotics of a public goods game model with diffusion
Klemens Fellner, Evangelos Latos, Takashi Suzuki
We consider a spatially inhomogeneous public goods game model with diffusion. By utilising a generalised Hamiltonian structure of the model we study the existence of global classic…
Global classical solutions to quadratic systems with mass control in arbitrary dimensions
Klemens Fellner, Jeff Morgan, Bao Quoc Tang
The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (sl…
On hysteresis-reaction-diffusion systems: Singular fast-reaction limit derivation and nonlinear hysteresis feedback
Klemens Fellner, Christian Münch
This paper concerns a general class of PDE-ODE reaction-diffusion systems, which features a singular fast-reaction limit towards a reaction-diffusion equation coupled to a scalar h…