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Shock waves and diffusion waves. (English) Zbl 0607.76064
Nonlinar systems of partial differential equations in applied mathematics, Proc. SIAM-AMS Summer Semin., Santa Fe/N.M. 1984, Lect. Notes Appl. Math. 23, Pt. 1, 283-291 (1986).
[For the entire collection see Zbl 0579.00008.]
The author, a specialist in conservation laws [see e.g.: S. S. Antman and the author, Quart. Appl. Math. 36, 377-399 (1979; Zbl 0408.73043) and the author, J. Differ. Equations 33, 92-111 (1979; Zbl 0379.35048)], describes recent progress on the study of the nonlinear stability and instability of shock waves and explains the importance of the role played by diffusion waves. He is also one of the co-authors of S. S. Antman, J. L. Ericksen, D. Kinderlehrer and I. Müller (eds.), Metastability and incompletely posed problems, Proc. Workshop, Menneapolis/Minn. 1984/85, IMA Vol. Math. Appl. 3 (1987; Zbl 0604.00008).
Reviewer: P.T.Crăciunaş
MSC:
76L05 Shock waves and blast waves in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B40 Asymptotic behavior of solutions to PDEs
35L65 Hyperbolic conservation laws
74M20 Impact in solid mechanics