Analytic solutions of a parabolic evolution system of partial differential equations coupled with a hyperbolic equation. (English) Zbl 0933.35005

The author studies the local existence, uniqueness and analyticity in time of solutions to a class of parabolic-hyperbolic systems consisting of parabolic equations coupled with a single hyperbolic equation (a continuity equation). As a special case, the system describes the motion of a compressible viscous fluid. First the author transforms the original system into the Lagrangian coordinate system. Then the author introduces a new Banach space, uses the analytic semigroup methods and the contraction mapping theorem to obtain a unique solution of the transformed system which is continuous for all \(t\) and analytic for all \(t\not=0\).
Reviewer: S.Jiang (Beijing)


35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B65 Smoothness and regularity of solutions to PDEs
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