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]**E. 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**34**#6293. MR**0206474 (34:6293)****[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**36**#5509. MR**0222457 (36:5509)****[5]**Kyuya Masuda,*On the exponential decay of solutions for some partial differential equations*, J. Math. Soc. Japan**19**(1967), 82-90. MR**34**#4663. MR**0204827 (34:4663)****[6]**S. L. Sobolev,*Applications of functional analysis in mathematical physics*, Izdat. Leningrad. Gos. Univ., Leningrad, 1950; English transl., Transl. Math. Monographs, vol. 7, Amer. Math. Soc., Providence, R. I., 1963. MR**14**, 565; MR**29**#2624. MR**0165337 (29:2624)**

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