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Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation. (English) Zbl 0371.35030


MSC:

35L15 Initial value problems for second-order hyperbolic equations
35L60 First-order nonlinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
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[2] Matsumura, A., On the asymptotic behavior of solutions of semilinear wave equations, Publ. RIMS, Kyoto Univ., 12 (1976), 169-189. · Zbl 0356.35008
[3] Mizohata, S., Theory of partial differential equations, Cambridge UP., 1973. · Zbl 0263.35001
[4] - 3 Quelque problemes au bord, du type mixte, pour des equations hyperboliques. Seminaire sur les equations aux derivees partielles, College de France, (1966-1967), 23-60.
[5] Nirenberg, L., On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa., 13 (1959), 115-162. · Zbl 0088.07601
[6] Nishida, T., Global smooth solutions for the second-order quasilinear wave equations with the first-order dissipation (to appear).
[7] Sattinger, D., Stability of nonlinear hyperbolic equations, Arch. Rational Mech. Anal., 28 (1968), 226-244. · Zbl 0157.17201
[8] Rabinowitz, P., Periodic solutions of nonlinear partial differential equations, Comm. Pure Appl. Math., 20 (1967), 145-205. · Zbl 0152.10003
[9] 9 Periodic solutions of nonlinear partial differential equations II, Comm. Pure Appl. Math., 22 (1969), 15-39. · Zbl 0157.17301
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