Existence of weak solutions to a class of fourth order partial differential equations with Wasserstein gradient structure

Autor:	Loibl, Daniel, Matthes, Daniel, Zinsl, Jonathan
Rok vydání:	2015
Předmět:	Mathematics - Analysis of PDEs Primary: 35K30 Secondary: 35A15 35D30
Druh dokumentu:	Working Paper
Popis:	We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure of the equation with respect to the $L^2$-Wasserstein distance on the space of probability measures. We construct a weak solution by approximation via the time-discrete minimizing movement scheme; necessary compactness estimates are derived by entropy-dissipation methods. Our theory essentially comprises the thin film and Derrida-Lebowitz-Speer-Spohn equations. Comment: 17 pages, no figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1507.05507 Zobrazit plný text záznamu View this record from Arxiv