Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Local energy decay for the damped plate equation in exterior domains


Author: Song Jiang
Journal: Quart. Appl. Math. 50 (1992), 257-272
MSC: Primary 35C15; Secondary 35L20, 43A50, 73F15, 73K10
DOI: https://doi.org/10.1090/qam/1162275
MathSciNet review: MR1162275
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We establish a rate of local energy decay for solutions of the damped plate equation with variable coefficients in exterior domains by using the spectral analysis to the corresponding stationary problem.


References [Enhancements On Off] (What's this?)

  • [1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975 MR 0450957
  • [2] S. Agmon, Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton, NJ, 1965 MR 0178246
  • [3] H. Iwashita and Y. Shibata, On the analyticity of spectral functions for some exterior boundary value problems, Glasnik Math. 23, 291-313 (1988) MR 1012030
  • [4] S. Jiang, $ L^{P}$ -- $ L^{q}$ estimates for solutions to the damped plate equation in exterior domains, Results in Math. 18, 231-253 (1990) MR 1078420
  • [5] S. Klainerman and G. Ponce, Global, small amplitude solutions to nonlinear evolution equations, Comm. Pure Appl. Math. 36, 133-141 (1983) MR 680085
  • [6] R. Leis, Initial Boundary Value Problems in Mathematical Physics, Teubner, Stuttgart, and Wiley, Chichester, 1986 MR 841971
  • [7] T. Muramatsu, On Besov spaces and Sobolev spaces of generalized functions defined in a general region, Publ. Res. Inst. Math. Sci. 9, 325-396 (1977) MR 0341063
  • [8] G. Ponce, Global existence of small solutions to a class of nonlinear evolution equations, Nonlinear Anal. 9, 399-418 (1985) MR 785713
  • [9] R. Racke, Decay rates for solutions of damped systems and generalized Fourier transforms, J. Reine Angew. Math. 412, 1-19 (1990) MR 1078997
  • [10] Y. Shibata, On the global existence of classical solutions of second order fully nonlinear hyperbolic equations with first order dissipation in the exterior domain, Tsukuba J. Math. 7, 1-68 (1983) MR 703667
  • [11] Y. Shibata and Y. Tsutsumi, On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain, Math. Z. 191, 165-199 (1986) MR 818663
  • [12] B. R. Vainberg, On the analytical properties of the resolvent for a certain class of operator-pencils, Math. USSR-Sb. 6, 241-273 (1968) MR 0240447
  • [13] B. R. Vainberg, On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behaviour for large time of solutions of nonstationary problems, Math. USSR-Sb. 21, 221-239 (1973)
  • [14] B. R. Vainberg, On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $ t \to \infty $ of solutions of non-stationary problems, Russian Math. Surveys 30, 1-58 (1975) MR 0415085
  • [15] C. H. Wilcox, Scattering theory for the d'Alembert equation in exterior domains, Lecture Notes in Math., vol. 442, Springer-Verlag, Berlin, 1975 MR 0460927

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35C15, 35L20, 43A50, 73F15, 73K10

Retrieve articles in all journals with MSC: 35C15, 35L20, 43A50, 73F15, 73K10


Additional Information

DOI: https://doi.org/10.1090/qam/1162275
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society