Partial Differential Equations

Existence of a solution to Lamb’s initial-boundary value problem with a limiting value of Poisson’s ratio

A. V. Kravtsov

Faculty of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

Abstract: The paper considers a Lamb’s initial-boundary value problem for an elastic half-space in the case when Poisson’s ratio takes the limiting value of 1/2. The existence of a classical solution in the form of an iterated improper integral in the case of axial symmetry is proved.

Key words: elastic medium, Lamé equations, Poisson’s ratio, Fourier–Bessel integral, Mellin integral, estimates of integrals.

UDC: 519.634

Received: 14.04.2023
Revised: 14.04.2023
Accepted: 26.06.2023

DOI: 10.31857/S0044466923100083

 English version: Computational Mathematics and Mathematical Physics, 2023, 63:10, 1848–1859

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