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

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.