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Periodic solutions to nonlinear one dimensional wave equation with  -dependent coefficients
Author(s):
V.
Barbu;
N.
H.
Pavel
Journal:
Trans. Amer. Math. Soc.
349
(1997),
2035-2048.
MSC (1991):
Primary 35L70, 35B10, 35L05
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Abstract:
This paper deals with  -periodicity and regularity of solutions to the one dimensional nonlinear wave equation with  -dependent coefficients
References:
- 1.
- A. Bahri and H. Brézis, Periodic solution of a nonlinear wave equation, Proc. Roy. Soc. Edinburgh Sect. A 1-D 85 (1980), 313-320. MR 82f:35011
- 2.
- A. Bamberger, G. Chavent and P. Lailly, About the stability of the inverse problem in wave equations; applications to the interpretation of seismic profiles, Appl. Math. Optimiz. 5 (1979), 1-47. MR 80b:86002
- 3.
- V. Barbu and N. H. Pavel, An inverse problem for the one dimensional wave equation, SIAM J. Control and Optimiz. 35-5 (1997), to appear.
- 4.
- H. Brézis, Periodic solutions of nonlinear vibrating strings and duality principles, Bull. AMS 8 (1983), 409-426. MR 84e:35010
- 5.
- H. Brézis and L. Nirenberg, Forced vibrations for a nonlinear wave equation, Comm. Pure Appl. Math. 31 (1978), 1-30. MR 81i:35112
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- 7.
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- 8.
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- 9.
- P. Rabinowitz, Free vibrations for a semilinear wave equation, Comm. Pure Appl. Math. 31 (1978), 31-68. MR 84i:35109
- 10.
- K. Yosida, Functional analysis, 6th ed., Springer-Verlag, Berlin, 1980. MR 82i:46002
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Additional Information:
V.
Barbu
Affiliation:
Department of Mathematics, University of Iasi, Iasi, Romania
Email:
barbu@uaic.ro
N.
H.
Pavel
Affiliation:
Department of Mathematics, Ohio University, Athens, Ohio 45701
Email:
npavel@bing.math.ohiou.edu
DOI:
10.1090/S0002-9947-97-01714-5
PII:
S 0002-9947(97)01714-5
Keywords:
Forced vibrations of nonhomogeneous strings,
propagation of seismic waves,
eigenvalues and eigenfunctions,
Fourier series,
subdifferentials,
maximal monotone operators,
Sobolev spaces
Received by editor(s):
April 18, 1995
Received by editor(s) in revised form:
December 4, 1995
Additional Notes:
This research was carried out while the first author was visiting Ohio University
Copyright of article:
Copyright
1997,
American Mathematical Society
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