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MATHEMATICS AND INFORMATICS*

ANNOUNCEMENT FOR 1996

Advanced Course on Theory of Elasticity

Date: 29 October-8 November 1996

Location: TICMI (Tbilisi, Telavi)

**David Gordeziani** (University of Tbilisi, Georgia)

I.VEKUA'S VERSION OF THE THEORY OF PLATES AND SHELLS

**Summary:** Reduction of three-dimensional problems of the theory of elasticity to the two-and one-dimensional mathematical models by Vekua's reduction method. Analysis of the models, their accuracy, and comparison with other models (variational-difference and finite elements methods, method of complex variables, justification of methods) (7 hours).

**George C. Hsiao** (University of Delaware, USA) Wolfgang L. Wendland (University Stuttgart, Germany)

BOUNDARY INTEGRAL EQUATIONS METHODS FOR EXTERIOR BOUNDARY VALUE PROBLEMS

**Summary:** The variational formulation of boundary integral equations and its connection to variational solutions of partial differential equations. Radiation conditions for exterior problems and their incorporation into boundary integral methods. Coerciveness properties, transmission problems, coercive boundary integral equations (4 hours).

SMALL FREQUENCY ASYMPTOTIC FOR BOUNDARY INTEGRAL EQUATION METHODS

**Summary:** Acoustic scattering, the Stokes expansion for exterior flows, scattering problems with elastic vibrations (4 hours).

ON THE COUPLING OF HYBRID FINITE AND BOUNDARY ELEMENT METHODS

**Summary:** Trefftz elements, hybrid macroelements, mortal elements, relaxed continuity requirements, coerciveness inequalities and error estimates, iterative solution techniques and parallelization (4 hours).

**David Natroshvili** (Georgian Technical university, Tbilisi, Georgia)

MATHEMATICAL PROBLEMS OF ANISOTROPIC ELASTICITY

**Summary:** Investigation of steady state oscillation problems for anisotropic media: fundamental matrices and properties of potentials, properties of boundary integral operators; generalised Sommerfeld-Kupradze type radiation conditions in anisotropic elasticity; uniqueness and existence theorems of solutions to the basic, interface, mixed and cracked pipe boundary value problems (7 hours).

**Coordinator:**
George Jaiani

**Deadline for registration:** September 20, 1996.

Further information:

Tbilisi International Centre of Mathematics and Informatics, I. Vekua Institute of Applied Mathematics of Tbilisi State University, University Str.2, Tbilisi - 43, Republic of Georgia

e-mail: jaiani@viam.sci.tsu.ge (George Jaiani)

Tel.: (+995 32) 305995

This is the first of a series of courses, at a level suitable for advanced graduate students or recent Ph.D.'s, which the TICMI plans to offer every year at fall.