Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-16T17:59:44.240Z Has data issue: false hasContentIssue false

On some quasilinear wave equations with dissipative terms

Published online by Cambridge University Press:  22 January 2016

Yoshio Yamada*
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we consider the initial value problems for the following quasilinear wave equations with dissipative terms

with initial conditions

where

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[1] Dickey, R. W., Infinite systems of nonlinear oscillation equations related to the string, Proc. Amer. Math. Soc., 23 (1969), 459468.Google Scholar
[2] Dickey, R. W., Infinite systems of nonlinear oscillation equations with linear damping, SIAM J. Appl. Math., 19 (1970), 208214.Google Scholar
[3] Dickey, R. W., The initial value problem for a nonlinear semi-infinite string, Proc. Roy. Soc. Edinburgh, 82 (1978), 1926.CrossRefGoogle Scholar
[4] Lions, J. L., On some questions in boundary value problems of mathematical physics, Contemporary Developments in Continuum Mechanics and Partial Differential Equations, (ed. by de La Penha, G. M. and Medeiros, L. A.), North-Holland, 1978.Google Scholar
[5] Matsumura, A., Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first order dissipation, Publ. RIMS, Kyoto Univ., 13 (1977), 349379.Google Scholar
[6] Menzala, G. P., Une solution d’une équation non linéaire d’évolution, C. R. Acad. Sc. Paris, 286 (1978), 273275.Google Scholar
[7] Menzala, G. P., On classical solutions of a quasilinear hyperbolic equation, Memórias de Matemática da Universidade Federal do Rio de Janeiro, 1978.Google Scholar
[8] Mizohata, S., The Theory of Partial Differential Equations, Cambridge University Press, 1973.Google Scholar
[9] Nirenberg, L., On elliptic partial differential equations, Ann. Scuola. Norm. Sup. Pisa, 13 (1959), 115162.Google Scholar
[10] Pohozaev, S. I., On a class of quasilinear hyperbolic equations, Math. USSR Sbornik, 25 (1975), 145158.Google Scholar
[11] Sobolev, S. L., Applications of Functional Analysis in Mathematical physics, Transl. Math. Monographs Vol. 7, A.M.S., 1963.Google Scholar
[12] Yamada, Y., On the decay of solutions for some nonlinear evolution equations of second order, Nagoya Math. J., 73 (1979), 6998.Google Scholar