SPECTRAL PROBLEMS IN ELASTICITY. SINGULAR BOUNDARY PERTURBATIONS

Authors

  • JAN SOKOLOWSKI INSTITUT ELIE CARTAN

Keywords:

SINGULAR PERTURBATIONS, SPECTRAL PROBLEM, ASYMPTOTICS OF EIGENFUNCTIONS AND EIGNEVALUES, ELASTICITY BOUNDARY VALUE PROBLEM

Abstract

THE THREE-DIMENSIONAL SPECTRAL ELASTICITY PROBLEM IS
STUDIED IN AN ANISOTROPIC AND INHOMOGENEOUS SOLID WITH SMALL
DEFECTS, I.E., INCLUSIONS, VOIDS, AND MICROCRACKS. ASYMPTOTICS OF
EIGENFREQUENCIES AND THE CORRESPONDING ELASTIC EIGENMODES ARE
CONSTRUCTED AND JUSTIFIED. NEW TECHNICALITIES OF THE ASYMPTOTIC ANALYSIS ARE RELATED TO
VARIABLE COEFFICIENTS OF DIFFERENTIAL OPERATORS, VECTORIAL SETTING
OF THE PROBLEM, AND USAGE OF INTRINSIC INTEGRAL CHARACTERISTICS OF
DEFECTS. THE ASYMPTOTIC FORMULAE ARE DEVELOPED IN A FORM CONVENIENT
FOR APPLICATION IN SHAPE OPTIMIZATION AND INVERSE PROBLEMS.

Author Biography

JAN SOKOLOWSKI, INSTITUT ELIE CARTAN

PROFESSOR OF APPLIED MATHEMATICS

UNIVERSITY HENRI POINCARE NANCY 1

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Published

2011-03-22

Issue

Vol. 8 No. 1 (2011)

Section

Articles

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