Exponential decay of weak solutions for hyperbolic systems of first order with discontinuous coefficients
Author:
Hang Chin Lai
Journal:
Trans. Amer. Math. Soc. 170 (1972), 425-436
MSC:
Primary 35L45
DOI:
https://doi.org/10.1090/S0002-9947-1972-0313640-2
MathSciNet review:
0313640
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The weak solution of the Cauchy problem for symmetric hyperbolic systems with discontinuous coefficients in several space variables satisfying the fact that the coefficients and their first derivatives are bounded in the distribution sense is identically equal to zero if it is exponential decay.
- [1] Edward D. Conway, Generalized solutions of linear differential equations with discontinuous coefficients and the uniqueness question for multidimensional quasilinear conservation laws, J. Math. Anal. Appl. 18 (1967), 238–251. MR 0206474, https://doi.org/10.1016/0022-247X(67)90054-6
- [2] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. 2: Partial differential equations (Vol. 2 by R. Courant), Interscience, New York, 1962. MR 25 #4216.
- [3] I. M. Gel'fand, Some questions of analysis and differential equations, Uspehi Mat. Nauk 14 (1959), no. 3 (87), 3-19; English transl., Amer. Math. Soc. Transl. (2) 26 (1963), 201-219. MR 22 #12294; MR 27 #1694.
- [4] A. E. Hurd and D. H. Sattinger, Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients, Trans. Amer. Math. Soc. 132 (1968), 159–174. MR 0222457, https://doi.org/10.1090/S0002-9947-1968-0222457-8
- [5] Kyûya Masuda, On the exponential decay of solutions for some partial differential equations, J. Math. Soc. Japan 19 (1967), 82–90. MR 0204827, https://doi.org/10.2969/jmsj/01910082
- [6] S. L. Sobolev, Applications of functional analysis in mathematical physics, Translated from the Russian by F. E. Browder. Translations of Mathematical Monographs, Vol. 7, American Mathematical Society, Providence, R.I., 1963. MR 0165337
Retrieve articles in Transactions of the American Mathematical Society with MSC: 35L45
Retrieve articles in all journals with MSC: 35L45
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1972-0313640-2
Keywords:
Hyperplane,
derivative in distribution sense,
weak solution,
mollifier method,
smoothed functions
Article copyright:
© Copyright 1972
American Mathematical Society
