Global solutions of a free boundary problem via mass transport inequalities

Gioia Carinci; Anna De Masi; Cristian Giardina'; Errico Presutti

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arXiv · 1402.5529

Global solutions of a free boundary problem via mass transport inequalities

Gioia Carinci·Anna De Masi·Cristian Giardina'·Errico Presutti

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Abstract

We study a free boundary problem which arises as the continuum version of a stochastic particles system in the context of Fourier law. Local existence and uniqueness of the classical solution are well known in the literature of free boundary problems. We introduce the notion of generalized solutions (which extends that of classical solutions when the latter exist) and prove global existence and uniqueness of generalized solutions for a large class of initial data. The proof is obtained by characterizing a generalized solution as the unique element which separates suitably defined lower and upper barriers in the sense of mass transport inequalities.

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BibTeX RIS

Gioia Carinci, Anna De Masi, Cristian Giardina', Errico Presutti. 2014-02-22. Global solutions of a free boundary problem via mass transport inequalities. https://arxiv.org/abs/1402.5529

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