From the 1 of 5 linked papers with an AI index.
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From diffusion to transmission via EDP-convergence: a paradigmatic multiscale limit
Thomas Frenzel, Alexander Mielke
The paper analyzes how nonlinear diffusion equations with a highly localized diffusion coefficient converge, in the energy‑dissipation principle sense, to a transmission condition…
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…
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…
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-…