Abstract
In this chapter, the Dirichlet problem for the wave equation is studied in a domain in \(\mathbb {R}^{3}\) with a cavity of small diameter ε. We also discuss the wave equation in a domain with the boundary smoothed in a small neighbourhood of a conical point.
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References
V.G. Maz’ya, S.A. Nazarov, B.A. Plamenevskii, Asymptotic theory of elliptic boundary value problems in singularly perturbed domains, v. 1, Birkhäuser, Basel–Boston–Berlin, 2000.
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Nazarov, S. A., Plamenevskii, B. A., Elliptic Problems in Domains with Piecewise Smooth Boundaries, De Gruyter Exposition in Mathematics 13, Berlin-New York, 1994.
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Korikov, D., Plamenevskii, B., Sarafanov, O. (2021). Asymptotics of Solutions to Wave Equation in Singularly Perturbed Domains. In: Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains. Operator Theory: Advances and Applications(), vol 284. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-65372-9_7
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DOI: https://doi.org/10.1007/978-3-030-65372-9_7
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