On energy decay-nondecay problems for wave equations with nonlinear dissipative term in RN

Kiyoshi MOCHIZUKI; Takahiro MOTAI

doi:10.2969/jmsj/04730405

On energy decay-nondecay problems for wave equations with nonlinear dissipative term in R^N

Kiyoshi MOCHIZUKI, Takahiro MOTAI

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JOURNAL FREE ACCESS

1995 Volume 47 Issue 3 Pages 405-421

DOI https://doi.org/10.2969/jmsj/04730405

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Published: 1995 Received: September 13, 1993 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Bergh and J. Löfström, Interpolation Spaces, Springer-Verlag, 1976.
2) L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer-Verlag, 1983.
3) S. Klainerman, Remarks on the global Sobolev inequality in the Minkowski space Rⁿ⁺¹ Comm. Pure Appl. Math., 40 (1987), 111-116.
4) J. L. Lions and W. A. Strauss, Some nonlinear evolution equations, Bull. Soc. Math. France, 93 (1965), 43-96.
5) B. Marshall, W. A. Strauss and S. Wainger, L^p-L^q estimates for the Klein-Gordon equation, J. Math. Pures Appl., 59 (1980), 417-440.
6) A. Matsumura, Energy decay of solutions of dissipative wave equations, Proc. Japan Acad., 53 (1977), 232-236.
7) K. Mochizuki, Decay and asymptotics for wave equations with dissipative term, Lecture Notes in Phys., 39, 1975, Springer-Verlag, pp. 486-490.
8) K. Mochizuki, Scattering theory for wave equations with dissipative terms, Publ. Res. Inst. Math. Sci., Kyoto Univ., 12 (1976), 383-390.
9) K. Mochizuki, Scattering Theory for Wave Equations, (Japanese), Kinokuniya,1984.
10) T. Motai and K. Mochizuki, On asymptotic behaviors for wave equations with nonlinear dissipative term in R^N, in preparation.
11) T. Motai, On the Cauchy problem for the nonlinear Klein-Gordon equation with a cubic convolution, Tsukuba J. Math., 12 (1988), 353-369.
12) T. Motai, Asymptotic behavior of solutions to the Klein-Gordon equation with a nonlinear dissipative term, Tsukuba J. Math., 15 (1991), 151-160.
13) M. Nakao, Energy decay of the wave equation with a nonlinear dissipative term, Funkcial. Ekvac., 26 (1983), 237-250.
14) J. Rauch and M. Taylor, Decaying states of perturbed wave equation, J. Math. Anal. Appl., 54 (1976), 279-285.
15) W. A. Strauss, The Energy Method in Nonlinear Partial Differential Equations, Brasil Inst. Math. Pure e Aplicada, 1966.

Right : [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer-Verlag, 1976.
[2] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer-Verlag, 1983.
[3] S. Klainerman, Remarks on the global Sobolev inequality in the Minkowski space Rⁿ⁺¹ Comm. Pure Appl. Math., 40 (1987), 111-116.
[4] J. L. Lions and W. A. Strauss, Some nonlinear evolution equations, Bull. Soc. Math. France, 93 (1965), 43-96.
[5] B. Marshall, W. A. Strauss and S. Wainger, L^p-L^q estimates for the Klein-Gordon equation, J. Math. Pures Appl., 59 (1980), 417-440.
[6] A. Matsumura, Energy decay of solutions of dissipative wave equations, Proc. Japan Acad., 53 (1977), 232-236.
[7] K. Mochizuki, Decay and asymptotics for wave equations with dissipative term, Lecture Notes in Phys., 39, 1975, Springer-Verlag, pp. 486-490.
[8] K. Mochizuki, Scattering theory for wave equations with dissipative terms, Publ. Res. Inst. Math. Sci., Kyoto Univ., 12 (1976), 383-390.
[9] K. Mochizuki, Scattering Theory for Wave Equations, (Japanese), Kinokuniya,1984.
[10] T. Motai and K. Mochizuki, On asymptotic behaviors for wave equations with nonlinear dissipative term in R^N, in preparation.
[11] T. Motai, On the Cauchy problem for the nonlinear Klein-Gordon equation with a cubic convolution, Tsukuba J. Math., 12 (1988), 353-369.
[12] T. Motai, Asymptotic behavior of solutions to the Klein-Gordon equation with a nonlinear dissipative term, Tsukuba J. Math., 15 (1991), 151-160.
[13] M. Nakao, Energy decay of the wave equation with a nonlinear dissipative term, Funkcial. Ekvac., 26 (1983), 237-250.
[14] J. Rauch and M. Taylor, Decaying states of perturbed wave equation, J. Math. Anal. Appl., 54 (1976), 279-285.
[15] W. A. Strauss, The Energy Method in Nonlinear Partial Differential Equations, Brasil Inst. Math. Pure e Aplicada, 1966.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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