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Mathematical methods for studying discontinuous solutions of nonlinear hyperbolic systems of equations. (Математические методы изучения разрывных решений нелинейных гиперболических систем уравнений.) (Russian) Zbl 1282.35002

Lektsionnye Kursy NOTs 16. Moskva: Matematicheskiĭ Institut im. V. A. Steklova, RAN (ISBN 5-98419-037-X/pbk). 120 p. (2010).
These lectures concern first-order hyperbolic systems in one space dimension. The main topics are well-posedness of initial-boundary value problems, discontinuous solutions, properties and structure of the discontinuities, non-uniqueness caused by the discontinuities and applications in continuum mechanics.

MSC:

35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
35L40 First-order hyperbolic systems
35L67 Shocks and singularities for hyperbolic equations
35D30 Weak solutions to PDEs
35L60 First-order nonlinear hyperbolic equations
35L65 Hyperbolic conservation laws
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