5 papers
From diffusion to transmission via EDP-convergence: a paradigmatic multiscale limit
Thomas Frenzel, Alexander Mielke
We consider nonlinear diffusion equations on an interval where the diffusion coefficient in a small region near the center is scaled such that it approximates a transmission condit…
Degenerate Diffusions on Continuum Percolation and Hamilton-Jacobi-Bellman Equations
Rodrigo Bazaes, Alexander Mielke, Chiranjib Mukherjee
We study degenerate controlled diffusions and Hamilton--Jacobi--Bellman equations posed on genuine continuum percolation clusters. The diffusion is constrained to evolve inside the…
Derivation of the fourth-order DLSS equation with nonlinear mobility via chemical reactions
Alexander Mielke, André Schlichting, Artur Stephan
We provide a derivation of the one-dimensional fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretize…
Discrete-to-continuum limit for nonlinear reaction-diffusion systems via EDP convergence for gradient systems
Georg Heinze, Alexander Mielke, Artur Stephan
We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-…
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…