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MATHEMATICS AND INFORMATICS*

ANNOUNCEMENT FOR 1997

Advanced Course on Pseudodifferential Operators and

Their Applications 1

Date: 25 June-5 July 1997

Location: TICMI (Tbilisi)

**Roland Duduchava** (University of Tbilisi, Georgia)

PSEODODIFFERENTIAL EQUATIONS ON MANIFOLDS WITH SMOOTH BOUNDARY: SOLVABILITY, ASYMPTOTICS OF SOLUTIONS, APPLICATIONS

**Summary:** Pseudodifferential operators (PsDOs) on manifolds (definition, properties). Boundedness of PsDOs in anisotropic Sobolev spaces with weight. Factorisation of matrix elliptic symbols and Fredholm properties of PsDOs. Asymptotics of solutions to elliptic systems of pseudodifferential equations. Application to some problems in elasticity.

**B.-Wolfgang Schulze** (University of Potsdam, Germany)

THE PSEODO-DIFFERENTIAL CALCULUS FOR SINGULAR AND DEGENERATE OPERATORS

**Summary:** The lectures present the basic methods of PsDOs for solving elliptic and parabolic problems on configurations with singularities (conical, edge, corners, cuspidal etc.). Essential tools are the Mellin transform, meromorphic operator-valued symbols and weighted wedge Sobolev spaces with asymptotics. The calculus is aimed at constructing parametrices or inverses with the calculus and to illustrate the connection to concrete models in applied sciences.

Advanced Course on Theory of Elasticity 2

Date: 16-25 September 1997

Location: TICMI (Tbilisi)

**Veronique Lods, Gerard Tronel** (Universite P. et M.Curie, France)

THREE- AND TWO-DIMENSIONAL ELASTICITY

**Summary:** During the past decades, substantial progress has been made in the mathematical analysis of three-dimensional elasticity and in the understanding of the two-dimensional linear and nonlinear theories of plates and shells by means of the technique of asymptotic analysis. The lectures will thoroughly review these recent developments.

**Tamas Vashakmadze** (University of Tbilisi, Georgia)

ON THE CONSTRUCTION OF A MATHEMATICAL THEORY OF ANISOTROPIC NONHOMOGENEOUS ELASSTIC PLATES AND SHELLS

**Summary:** Construction of finite models (e.g. such as von Karman, Reissner, Kirchhoff, etc) without simplifying hypotheses. Investigation of problems of error estimation, convergence and effective solvability of two-dimensional models corresponding to the reduction methods (e.g. Theories of Vekua, Babushka). Some similar generalizations for piezoelastic and electric elastic plates and shells. New numerical processes for solving of some two-dimensional problems in above sense.

**Coordinator:**
George Jaiani

These courses are suitable for advanced graduate students or recent Ph.D.'s. The participants will also have an opportunity to give 20-minute talkes on their own work at a mini-symposium which will take place during the Advanced Course. Lectures and abstracts of the talks will be published and distributed among the lecturers and participants after Advanced Course. The registration fee for participants is 400 USD which includes all local expenses during the Advanced Course. A restricted number of participants will be awarded grants.

**Further information**: TICMI, I.Vekua Institute of Applied Mathematics of Tbilisi State University,University Str. 2, Tbilisi 380043, Georgia

e.mail: jaiani@viam.sci.tsu.ge

Tel.:+995 32 305995