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math.AP2026
Solutions to fourth order degenerate parabolic equations obtained via weighted energy dissipation
Daniel Matthes, Vera Pazukhina
We apply the variational method of Weighted Energy Dissipation (WED) to obtain a global-in-time approximation of solutions to fourth order degenerate parabolic equations of Cahn-Hi…
math.AP2026
Maximal monotonicity and contraction semigroup for the quantum drift-diffusion (Derrida-Lebowitz-Speer-Spohn) equation
Daniel Matthes, Giuseppe Savaré, André Schlichting
We study the quantum drift-diffusion, or Derrida-Lebowitz-Speer-Spohn (DLSS), equation for a nonnegative density on a bounded convex domain with Neumann boundary conditio…
math.AP2026
The Aronson-Bénilan estimate for a Lagrangian particle discretization of the Porous Medium Equation
Marco Di Francesco, Daniel Matthes
We consider a nearest neighbor, Lagrangian particle discretization of the one dimensional porous medium equation. We prove that the particle model satisfies a discrete analog of th…