Hyperbolic systems of conservation laws and the mathematical theory of shock waves : Based on lectures delivered at a regional conference held at the University of California at Los Angeles in September, 1971, arranged by the Conference Board of Mathemati

This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown. Hyberbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves......Page 1 Contents......Page 8 Preface......Page 10 1. Quasi-linear hyperbolic equations.......Page 12 2. Conservation laws.......Page 14 3. Single conservation laws.......Page 15 4. The decay of solutions as t tends to infinity.......Page 28 5. Hyperbolic systems of conservation laws.......Page 35 6. Pairs of conservation laws.......Page 44 Notes.......Page 52 REFERENCES......Page 58