Long-time existence of classical solutions to a 1-D swelling gel

2013/03/26 by M. Carme Calderer, Calderer, M. Carme, Robin Ming Chen +1
Mathematics · #35L50 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35L50 #msc:35R35

paper · pdf · doi:10.48550/arxiv.1303.6548

arxiv created 2013/03/26 · arxiv updated 2013/03/27

Abstract

In this paper we derived a model which describes the swelling dynamics of a gel and study the system in one-dimensional geometry with a free boundary. The governing equations are hyperbolic with a weakly dissipative source. Using a mass-Lagrangian formulation, the free-boundary is transformed into a fixed-boundary. We prove the existence of long time, continuously differentiable solutions to the transformed fixed boundary problem.

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