Global existence of solutions to a coupled parabolic-hyperbolic system with moving boundary

Choi, Y.; Miller, Craig

doi:10.1090/S0002-9939-2011-10801-3

Global existence of solutions to a coupled parabolic-hyperbolic system with moving boundary
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by Y. S. Choi and Craig Miller PDF

Proc. Amer. Math. Soc. 139 (2011), 3257-3270 Request permission

Abstract:

A cell motility study leads to a moving boundary problem governed by a system of parabolic-hyperbolic equations. Establishing the parabolicity of one of the governing equations requires a priori bound analysis. Such bounds also exclude the formation of shock in the hyperbolic equation. Speeds of the moving boundaries can then be controlled, which eventually leads to the global existence of solutions.

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