Giorgi Baghaturia

We consider the Cauchy problem on the closed data support for one class quasi-linear equations of mixed type. We have proved that the Cauchy problem is well posed. The families of characteristic curves are described and the area of definition of the solution is constructed.

We consider the Cauchy problem on a closed data support for one class quasi-linear equations of mixed type. We have proved that the Cauchy problem is well posed. The families of characteristic curves are described and the area of definition of the solution is constructed. To solve the problem, a difference scheme is constructed, the approximation and stability of the scheme is studied. Calculation results are given for concrete examples.

Some Hyperbolic problems for quasi-linear equations of mixed type are considered.

One of many fields of scientific activity of academician Yanenko was searching for special solutions of PDE’s, especially for solutions with degenerate hodograph of Euler equations of gas-dynamics. The simplest example is given by so called double waves.The solutions are mappings of R3 into R3 in general of rank 3. However, there are also solutions of rank 1 - simple waves and rank 2 - double waves.When searching for double waves one can determine at first the 2-dimensional hodograph surface S, which is the set of values of the double wave solution. The double wave hodographs are rather exceptional surfaces.

For one class of quasi-linear partial differential equation a non-linear version of Inverse Problem is considered, The problem is solved by using of characteristic invariants. In some cases the problem is reduced to characteristic Goursat problem and the algorythm for finding of numerical solution of Goursat problem is constructed.

For one class of quasi-linear partial differential equation a non-linear version of Inverse Problem is considered, The problem is solved by using of characteristic invariants. In some cases the problem can be reduced to characteristic Goursat problem and the algorythm for finding of numerical solution of Goursat problem is constructed.

For some classes of quasi-linear partial differential equations general integrals are constructed, which have the form of sum of two arbitrary functions. Some non-linear variants of direct and inverse problems are posed and solved. Specific examples are also investigated and Domains of propagation of solutions are described.

For some classes of quasi-linear partial differential equation we constructed general integrals in the form of sum of two arbitrary functions. Some non-linear variants of inverse problem are posed and solved. Specific examples are also investigated and Domains of propagation of solutions are described.

Problem of Integrability of Some type of quasi-linear equations are considered. Solutions are constructed in the form of double waves. The concept of non-linear superposition of solutions is introduced

We solved a non-stationary problem when a semi-infinite crack propagates along the line of connection of two elastic strips having different characteristics of elasticity. We obtained the Solution of the problem of crack propagation in elastic strip by means of Fourier transform and the method of Wiener-Hopf.

We considered some non-classical problems for one class of quasi-linear partial differential equations. The theorems of existence and uniqueness of solutions are proved and domains of definitions of solutions are described.

For some quasi-linear partial differential equations a non-linear version of Characteristic Problem is considered. The problem is solved by using of characteristic invariants. The Analogue of Assgeirson theorem is proved.

For one class of quasi-linear partial differential equation we constructed general integrals by means of a characteristic method. The general integral is constructed in the form of sum of two arbitrary functions. Some specific examples are also investigated Domains of propagation of solutions are described.

For one class of quasi-linear partial differential equation a non-linear version of Cauchy Problem is considered, The problem is solved by using of characteristic invariants and the algorythm for finding of numerical solution is constructed.

For one class of quasi-linear partial differential equation a non-linear version of Cauchy Problem is considered, The problem is solved by using of characteristic invariants and the algorythm for finding of numerical solution is constructed.

Problem of Integrability of Hydrodynamic type of equations are considered. Solutions are constructed in the form of double waves.

We solved anti plane problem when a semi-infinite crack propagates along the line of connection of two elastic strips having different characteristics of elasticity. We obtained the Solution of the problem of crack propagation in elastic strip by means of Fourier transform and the method of Wiener-Hopf.

For one class of quasi-linear partial differential equation a non-linear version of Cauchy Problem is considered, when the support of initial data is a closed curve. The problem is solved by using of characteristic invariants.

For one class of quasi-linear partial differential equation a non-linear version of Cauchy Problem is considered, when the support of initial data is a closed curve. The problem is solved by using of characteristic invariants.

For a quasi-linear partial differential equation a non-linear version of Cauchy Problem is considered, when the support of initial data is a closed curve. The problem is solved by using of characteristic invariants.

For one quasi-linear partial differential equation a version of non-local Problem is considered. The problem is solved by using of characteristic invariants.

The structure of the characteristic areas of the mixed type equation is studied.

For one quasi-linear partial differential equation a non-linear version of Goursat Problem is considered, when one characteristic is unknown. The problem is solved by using of characteristic invariants.

Doctoral Thesis Referee

Master Theses Supervisor

Doctoral Thesis Supervisor/Co-supervisor

Scientific editor of monographs in foreign languages

Scientific editor of a monograph in Georgian

Editor-in-Chief of a peer-reviewed or professional journal / proceedings

Review of a scientific professional journal / proceedings

Member of the editorial board of a peer-reviewed scientific or professional journal / proceedings

Participation in a project / grant funded by an international organization

Participation in a project / grant funded from the state budget

Patent authorship

Membership of the Georgian National Academy of Science or Georgian Academy of Agricultural Sciences

Membership of an international professional organization

Membership of the Conference Organizing / Program Committee

National Award / Sectoral Award, Order, Medal, etc.

Honorary title

Monograph

Handbook

Research articles in high impact factor and local Scientific Journals

Publication in Scientific Conference Proceedings Indexed in Web of Science and Scopus