Kulikovskiĭ, A. G.; Sveshnikova, E. I.; Chugaĭnova, A. P. 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. Reviewer: Lutz Recke (Berlin) Cited in 6 Documents 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 Keywords:weak discontinuities; one space dimension; non-uniqueness caused by the discontinuities PDF BibTeX XML Cite \textit{A. G. Kulikovskiĭ} et al., Математические методы изучения разрывных решений нелинейных гиперболических систем уравнений (Russian). Moskva: Matematicheskiĭ Institut im. V. A. Steklova, RAN (2010; Zbl 1282.35002) Full Text: DOI Link OpenURL