A generalized Cauchy problem for the linear differential equations of coupled physical-mechanical fields
type: Item
instance of: scholarly article
title: A generalized Cauchy problem for the linear differential equations of coupled physical-mechanical fields
zbMATH Open document ID: 0644.35013
DOI: 10.1016/0021-8928(85)90007-3
author: R. I. Mokrik
author: Yu. Pyryev
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: A generalised Cauchy problem for a partial differential equation with constant coefficients, which is encountered in the study of physical processes in continuous media with widened physical-mathematical fields is considered. The characteristic properties of the solution of the problem, under certain constraints imposed on an equation by the stability condition, are studied. The presence of waves of higher and lower order is characteristic for the solution; in the course of time the lower-order waves are maintained and take a characteristic form. In the general case, the solution is represented in the form of integrals over the segments which link the singular points of Fourier-Laplace transforms with respect to time of the solution under consideration. The methods proposed enable an exact investigation to be made of the processes described by the equation for any time constants, and they also enable one to isolate the singularities at the fronts of propagating perturbations. As an application, the dynamic processes taking place in a thermoelastic subspace as a result of applying a mechanical and a thermal input at the boundary is studied. It is shown that in the case of unit perturbation of the boundary, the stress and temperature waves in the course of time assume a bell-shaped form and propagate with adiabatic velocity. A numerical analysis of the process which occurs due to sudden application of the force and of the thermal shock at the boundary is given.
Mathematics Subject Classification ID: 35E15
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 4050094
zbMATH Keywords: Cauchy problem
zbMATH Keywords: constant coefficients
zbMATH Keywords: continuous media
zbMATH Keywords: waves of higher and lower order
zbMATH Keywords: singular points of Fourier-Laplace transforms
zbMATH Keywords: singularities
zbMATH Keywords: propagating perturbations
zbMATH Keywords: stress and temperature waves
reviewed by: Pierre Bolley
MaRDI profile type: Publication
full work available at URL: 0021-8928(85)90007-3
OpenAlex ID: W2010841000
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description: scientific article; zbMATH DE number 4050094