Hokkaido Mathematical Journal

Sufficient conditions for decay estimates of the local energy and a behavior of the total energy of dissipative wave equations in exterior domains

Mishio KAWASHITA

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Abstract

Decaying properties of the local energy for the dissipative wave equations with the Dirichlet boundary conditions in exterior domains are discussed. For the dissipation coefficient, natural conditions ensuring that waves trapped by obstacles may lose their energy are considered. Under this setting, two sufficient conditions for getting the decay estimates for the energy in bounded regions (i.e. the local energy) are given. These conditions bring some relaxation on classes of the dissipation coefficient which uniformly decaying estimates for the local energy hold. Further, decaying properties of the total energy are also discussed.

Article information

Source
Hokkaido Math. J., Volume 46, Number 3 (2017), 277-313.

Dates
First available in Project Euclid: 7 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1510045300

Digital Object Identifier
doi:10.14492/hokmj/1510045300

Mathematical Reviews number (MathSciNet)
MR3720331

Zentralblatt MATH identifier
06814865

Subjects
Primary: 35L05: Wave equation 35B40: Asymptotic behavior of solutions

Keywords
Dissipative wave equations exterior problems local energy decay total energy decay non-compactly supported initial data

Citation

KAWASHITA, Mishio. Sufficient conditions for decay estimates of the local energy and a behavior of the total energy of dissipative wave equations in exterior domains. Hokkaido Math. J. 46 (2017), no. 3, 277--313. doi:10.14492/hokmj/1510045300. https://projecteuclid.org/euclid.hokmj/1510045300


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