On the motion of a viscoelastic solid in presence of a rigid wall. I. Darboux and general Cauchy problems for a third-order hyperbolic operator: Explicit Riemann function and maximum principles
type: Item
instance of: scholarly article
title: On the motion of a viscoelastic solid in presence of a rigid wall. I. Darboux and general Cauchy problems for a third-order hyperbolic operator: Explicit Riemann function and maximum principles
zbMATH Open document ID: 0534.73032
DOI: 10.1007/BF00944706
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1983-01-01T00:00:00Z
review text: The authors concentrate on extending the Riemann representation method to the (*) equation for unidimensional motion of a standard linear solid in absence of external forces and prove that the Riemann function is substantially characterized by the fundamental solution of that operator equation. The Darboux and Cauchy problems related to (*) are solved. Some theorems concerning inversion formulae of Laplace transforms, the minimum principle etc. are dealt with and seem to be of good originality. Results of the theorems given in the paper are further extended. The paper is well presented. It would be of interest to those working on structural problems. It is really a good piece of research work.
Mathematics Subject Classification ID: 74D99
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35L85
zbMATH DE Number: 3848711
zbMATH Keywords: rigid wall
zbMATH Keywords: third-order hyperbolic operator
zbMATH Keywords: viscoelastic standard linear solid operator
zbMATH Keywords: compatibility
zbMATH Keywords: asymptotic
zbMATH Keywords: perturbation
zbMATH Keywords: Riemann function characterized by fundamental solution
zbMATH Keywords: extending the Riemann representation method
zbMATH Keywords: equation for unidimensional motion of a standard linear solid
zbMATH Keywords: absence of external forces
zbMATH Keywords: Darboux and Cauchy problems
zbMATH Keywords: inversion formulae of Laplace transforms
zbMATH Keywords: minimum principle
author: B. D'Acunto
author: Armando D'Anna
author: Pasquale Renno
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3848711