Preprint: Derivation of the fourth-order DLSS equation with nonlinear mobility via chemical reactions

8 October 2025

Together with Alexander Mielke and Artur Stephan, we provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider the rate equation on the discretized circle for a process in which pairs of particles occupying the same site simultaneously jump to the two neighboring sites; the reverse process involves pairs of particles at adjacent sites simultaneously jumping back to the site located between them. Depending on the rates, in the vanishing-mesh-size limit we obtain either the classical DLSS equation or a variant with nonlinear mobility of power type.

Numerically obtained source-type solution for the fourth order DLSS_α equation with nonlinear mobility α>1 — Numerically obtained source-type solution for the fourth order DLSS $_\alpha$ equation with nonlinear mobility $\alpha>1$

Now accepted in SIAM Journal on Mathematical Analysis.

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