*Reports of
Enlarged Session of the Seminar of I. Vekua Institute
of Applied Mathematics*

Volume 12, # 1-3, 1997

This collection contains
the reports which were delivered on April 21-23, 1997 at the sections of
Partial Differential Equations and mechanics of deformable rigid bodies of
enlarged session of the seminar of I. Vekua Institute
of Applied Mathematics.

Chairman of sections

*G. Jaiani*

*M. Basheleishvili*

*D. Gordeziani*

* *Edited by

*T. Jangveladze*

*Ts. Gabeskiria*

*R. Bochorishvili*

C O N T E N T S

# 1

**Chichua**** G.** On a Stability of an Approximate Solution for
Solid-fluid Model

**Jaiani**** G.** On a Modification of Lax-Milgram
Theorem

**Jangveladze**** T.** On the Asymptotic Behaviour
as t → ∞ Of Solutions of One Nonlinear Integro-Differential Parabolic Equation

**Kvashilava**** G.** One Spatial Boundary Value Problem of Darboux Type for the Third Order Hyperbolic Equation

**Klebanskaya**** M.** Darboux Problem for
Hyperbolic Equation with Parabolic Degeneracy

**Midodashvili**** B.** On the Solvability of the One Nonlocal Problem for the Fourth Order Hyperbolic Equation

**Sharikadze**** J.** Three-Dimensional Boundary Layer Near the Line of Intersection of Two Porous Surfaces with
Heat Transfer

**Shulaia**** D.** On Spectral Representation of the
Linear Multigroup Transport Problem

**Tavkhelidze**** I.**

# 2

**Bitsadze**** L.** First Boundary Value Problem of the Electroelasticity for the Transversally Isotropic
Half-Plane with Curvilinear Cuts

**Khomasuridze**** I.**

# 3

**Bochorishvili**** R. **Three-point Semidiscrete
Moving Grid Schemes for Nonlinear Scalar Conservation Laws in One Space
Dimensions

**Bochorishvili**** R., Elkanishvili
N.** On Flux
Splitting for Ideal Gas Dynamic Equations

**Bukhnikashvili**** A.I.** Richardson's Iterated Method for
the Solution of Linear Equation with a Bounded Self-Conjugate Operator

**Davitashvili**** T.** Numerical Model for

**Geladze**** G.** The Numerical Simulation of Artificial
Influence the Humidity Processes

**Gordeziani**** D., Gordeziani N., Avalishvili G.** On the Investigation and Resolution
of Non-Local Boundary and Initial-Boundary Value Problems

**Meladze**** B.** On a Constraction of
Three-Level Schemes for Nonlinear Scalar Conservation Laws

**Rogava**** J., Kudava M.** On the Stability and Convergence of
Three-Layer Semi-Discrete Scheme for Quasi-Linear Abstract Hyperbolic Equation

**Skhirtladze**** R. **On Searching of Polynomial Conservation Laws
for Some Multidimensional Evolution Equations Using Generalized Euler Operator