Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation

Paolo Secchi

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 1, page 189-206
  • ISSN: 0392-4041

Abstract

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We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.

How to cite

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Secchi, Paolo. "Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation." Bollettino dell'Unione Matematica Italiana 7-B.1 (2004): 189-206. <http://eudml.org/doc/195728>.

@article{Secchi2004,
abstract = {We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.},
author = {Secchi, Paolo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {189-206},
publisher = {Unione Matematica Italiana},
title = {Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation},
url = {http://eudml.org/doc/195728},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Secchi, Paolo
TI - Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/2//
PB - Unione Matematica Italiana
VL - 7-B
IS - 1
SP - 189
EP - 206
AB - We consider the exterior problem in the plane for the wave equation with a Neumann boundary condition. We are interested to the asymptotic behavior for large times for the solution, and in particular to the dependence on the norms of the initial data in the estimate for the pointwise decay rate. In the paper we prove such an estimate, by a combination of the estimate of the local energy decay and decay estimates for the free space solution.
LA - eng
UR - http://eudml.org/doc/195728
ER -

References

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  6. LI, TA-TSIEN- CHEN, YUNMEI, Global classical solutions for nonlinear evolution equations, Longman, Harlow, 1992. Zbl0787.35002MR1172318
  7. MORAWETZ, C. S., Decay for solutions of the exterior problem for the wave equation, Comm. Pure Appl. Math., 28 (1975), 229-264. Zbl0304.35064MR372432
  8. MORAWETZ, C. S., Notes on time decay and scattering for some hyperbolic problems, Reg. Conf. Series Appl. Math., SIAM1975. Zbl0303.35002MR492919
  9. RACKE, R., Lectures on Nonlinear Evolution Equations, Initial Value Problems, Vieweg Verlag, 1992. Zbl0811.35002MR1158463
  10. RALSTON, J. V., Solutions of the wave equation with localized energy, Comm. Pure Appl. Math., 22 (1969), 807-824. Zbl0209.40402MR254433
  11. VAINBERG, B., On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as t → ∞ of solutions of non-stationary problems, Russian Math. Surveys, 30 (1975), 1-58. Zbl0318.35006MR415085

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