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Bassanini, Piero; Turo, Jan

Generalized solutions to free boundary problems for hyperbolic systems of functional partial differential equations. (English) Zbl 0716.35088

Ann. Mat. Pura Appl., IV. Ser. 156, 211-230 (1990).
Local generalized (almost everywhere) solutions to a free boundary (Stefan) problem for a quasilinear hyperbolic system of functional PDE’s of first order in two independent variables and diagonal form are investigated. The solution satisfies initial conditions and boundary conditions on the boundary of the domain and on the free boundary, tailored to hyperbolic free boundary and Stefan problems which arise from applications [as e.g. in C. Denson Hill, J. Math. Anal. Appl. 31, 117-129 (1970; Zbl 0203.410); M. Brokate, Numer. Funct. Anal. Optimization 5, 217-248 (1982; Zbl 0489.35078)]. The formulation includes retarded arguments and hereditary Volterra terms, as well as the case of shock wave problems.
Reviewer: P.Bassanini

Cited in 5 Documents

MSC:

35R35 Free boundary problems for PDEs
35L60 First-order nonlinear hyperbolic equations
35R10 Partial functional-differential equations

Keywords:

Stefan problems

Citations:

Zbl 0203.410; Zbl 0489.35078
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References:

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