10 citations · 17 across the 10 of their papers we have counts for
11 papers
Global classical solutions by transport noise for reaction-diffusion systems with entropy dissipation
Antonio Agresti, Michael Kniely, Bao Quoc Tang
The existence of global classical solutions for reaction-diffusion systems arising from chemical reaction networks remains a major open problem in the deterministic setting, especi…
Exponential equilibration of an electro-energy-reaction-diffusion system arising from a two-level semiconductor model
Michael Kniely
We consider a thermodynamically correct framework for electro-energy-reaction-diffusion systems, which feature a monotone entropy functional while conserving the total charge and t…
On the equilibrium solutions of electro-energy-reaction-diffusion systems
Katharina Hopf, Michael Kniely, Alexander Mielke
Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects…
Regularity of random elliptic operators with degenerate coefficients and applications to stochastic homogenization
Peter Bella, Michael Kniely
We consider degenerate elliptic equations of second order in divergence form with a symmetric random coefficient field . Extending the work of the first author, Fehrman, and Ott…
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 convergence to equilibrium for a family of drift-diffusion models with trap-assisted recombination and self-consistent potential
Klemens Fellner, Michael Kniely
We investigate a recombination-drift-diffusion model coupled to Poisson's equation modelling the transport of charge within certain types of semiconductors. In more detail, we stud…
Global existence analysis of energy-reaction-diffusion systems
Julian Fischer, Katharina Hopf, Michael Kniely +1
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest…
Variance reduction for effective energies of random lattices in the Thomas-Fermi-von Weizsäcker model
Julian Fischer, Michael Kniely
In the computation of the material properties of random alloys, the method of "special quasirandom structures" attempts to approximate the properties of the alloy on a finite volum…
New optimal control problems in density functional theory motivated by photovoltaics
Gero Friesecke, Michael Kniely
We present and study novel optimal control problems motivated by the search for photovoltaic materials with high power-conversion efficiency. The material must perform the first st…
Uniform convergence to equilibrium for a family of drift-diffusion models with trap-assisted recombination and the limiting Shockley--Read--Hall model
Klemens Fellner, Michael Kniely
We consider a family of drift-diffusion-recombination systems, where the recombination of electrons and holes is facilitated by an intermediate energy-level for electrons in so-cal…
Dual simulation of finite density lattice QED at large mass
Michael Kniely, Christof Gattringer
We discuss a mapping of lattice QED with two flavors and a chemical potential to dual variables, which are surfaces for the gauge fields and loops for the fermions. The gauge field…