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The Cauchy Problem of Couple-Stress Elasticity
by
Niyozov Ikbol
Department of Mathematics, Samarkand State Universitet, Uzbekistan
We study the Cauchy problem for the oscillation equation of the couple-stress theory of elasticity in a unbounded domain. Both the displacement and stress are given on a part S of the boundary of the domain. This problem is densely solvable while data of compact support in the interior of S fail to belong to the range of the problem. Hence the problem is ill-posed which makes the standard calculi of Fourier integral operators inapplicable. If S is real analytic the Cauchy-Kovalevskaya theorem applies to guarantee the existence of a local solution. We invoke the special structure of the oscillation equation to derive explicit conditions of global solvability and an approximation solution.
Date received: December 25, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavk-59.