A boundary value problem for quasilinear hyperbolic systems of hereditary partial differential equations. (English) Zbl 0624.35013
The paper deals with a boundary value problem for quasilinear differential-functional systems in the Schauder canonic form. The author proves, by means of the fixed point theorem in the product of two Banach spaces, existence, uniqueness and continuous dependence on boundary data of generalized solutions (in the “almost everywhere” sense). A few kinds of differential-integral systems and systems with a retarded argument can be obtained from the considered problem by specializing the operators in the differential-functional systems.
Reviewer: Z.Kamont
MSC:
35F30 | Boundary value problems for nonlinear first-order PDEs |
35L50 | Initial-boundary value problems for first-order hyperbolic systems |
35R10 | Partial functional-differential equations |
35D05 | Existence of generalized solutions of PDE (MSC2000) |
35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |