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Global existence of solutions to a coupled parabolic-hyperbolic system with moving boundary. (English) Zbl 1232.35197
The authors prove the existence of a unique smooth global solution to the system of parabolic-hyperbolic equations which arises in a cell motility study. The parabolicity of one of the governing equations is a consequence of a priori bounds which also exclude the formation of shock in the hyperbolic equation and enable us to control the moving boundaries.

MSC:
35R37 Moving boundary problems for PDEs
35M30 Mixed-type systems of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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