| XII International Conference of the Georgian Mathematical Union | Batumi, Georgia | 2022 | 29/08/2022 - 03/09/2022 | Georgian Mathematical Union, Batumi State University | On a Cauchy Problem with Closed Support of Data and its Discrete Analogue | oral | 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.
| http://gmu.gtu.ge/Batumi2022/ |
| XIII Annual International Meeting of the Georgian Mechanical Union | Batumi, Georgia | 2022 | 22/08/2022 - 26/08/2022 | Georgian Mechanical Union, Batumi State Maritime Academy, Akaki Tsereteli State University | On a Cauchy problem with closed support of data | oral | 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. | https://atsu.edu.ge/index.php/en/teqnikuri-news-eng/2776-xiii-conferencia-teqnikuri-eng#:~:text=CONTACT-,XIII%20Annual%20International%20Meeting%20of%20the%20Georgian%20Mechanical%20Union,Corona%20Virus%20situation%20in%20Georgia. |
| XII Annual International Meeting of the Georgian Mechanical Union. Dedicated to 130 birthday anniversary of academician N. Muskhelishvili | Kutaisi, Georgia | 2021 | 9-11 September | Georgian Mechanical Union, Kutaisi state University | Inverse problems for the second order equations of mixed type | oral | 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. | https://atsu.edu.ge/index.php/en/teqnikuri-news-eng/2349-meqanikosta-yovelwliuri-saert-konferencia-eng |
| XI Annual International Conference of the Georgian Mathematical Union | Batumi, Georgia | 2021 | 23-28 August | Georgian Mathematical Union, Batumi State University | Inverse Problems and Their Discrete Analogs for the Second Order Quasi-Linear Equations of Mixed Type | oral | 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. | http://gmu.gtu.ge/Batumi2021/ |
| XI Annual International Meeting of the Georgian Mechanical Union | Batumi, Georgia | 2020 | 27- 29 August | Georgian Mathematical Union, Batumi State University | Direct and inverse Cauchy problems for second-order equations of mixed type. | oral | 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. | https://atsu.edu.ge/index.php/en/teqnikuri-news-eng/1988-mqanikosta-kavshiris-saertashoriso-konferencia-eng |
| 12th International Conference on Computer Science and Information Technologies (CSIT) | Erevan, Armenia | 2019 | September 23–27 | National Academy of Sciences of the Republic of Armenia | Some Nonlinear Version of a Nonlocal Problem and Its Discrete Analogue | oral | Some Nonlinear Version of a Nonlocal Problem and Its Discrete Analogue are presented | IEEE Conference Publications, 2019, p. 77-78. DOI: 10.1109/CSITechnol.2019.8894943 |
| 16th Conference “Mathematics in Technical and Natural Sciences” | Kościelisko,Poland | 2019 | 30th June - 5th July | AGH University of Science and Technology | General Integrals and Inverse Problems for the Second Order Quasi-Linear Equations of Mixed Type. | oral | 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. | http://www.mtns.agh.edu.pl/ |
| X International Conference of the Georgian Mathematical Union | Batumi, Georgia | 2019 | September 2-6 | Georgian Mathematical Union, Batumi State University | On a Nonlocal Problem and its Discrete Analogy | oral | We investigate a nonlocal problem and its discrete analogue for non-strictly hyperbolic equation. We also considered the discrete analog of this problem and have proved the convergence theorems for the difference scheme. | http://gmu.ge/Batumi2019/ |
| CERN Cognitive Festival in Georgia | Tbilisi, Georgia | 2018 | October 22 – 26 | CERN; Georgian Technical University | Some Properties of Hadamard Matrices | oral | Some Properties of Hadamard Matrices is discussed | https://indico.cern.ch/event/766618/timetable/#20181025.detailed |
| 9th International Conference of the Georgian Mathematical Union | Batumi, Georgia | 2018 | September 3-7 | Georgian Mathematical Union, Batumi State University | Non-classical problems for second order quasi-linear equations with rectilinear characteristics | oral | 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. | http://www.gmu.ge/Batumi2018/ENG/index.html |
| 11th International Conference on Computer Science and Information Technologies (CSIT-2017) | Erevan, Armenia | 2017 | September 25–29 | National Academy of Sciences of the Republic of Armenia | Maximum inequalities and their applications to Hadamard matrices | oral | A new numerical characterization for Hadamard matrices is introduced. Its estimations for different norms are established by use of appropriate maximal inequalities for the signed vector summands. | https://csit.am/2017/ |
| VIII International Conference of the Georgian Mathematical Union | | 2017 | 4-8 September | Georgian Mathematical Union, Batumi State University | Non-linear versions of Characteristic Problems for the Second Order PDEs of Mixed Type. | oral | 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. | http://www.gmu.ge/Batumi2017/ |
| South Caucasus Computing and Technology Workshop (SCCTW 2016) | Tbilisi, Georgia | 2016 | October 3-7, 2016 | CERN; Georgian Technical University | On some applications of Hadamard matrices | oral | Some Applications of Hadamard Matrices are discussed | https://indico.cern.ch/event/572800/ |
| 4-th International Conference "Lie Groups, Differential Equations and Geometry" | Modica, Italy | 2016 | June 8-15 | Departmeny of Mathematics and Computer Science of the University of Palermo | On the geometry of the domain of the solution of nonlinear Cauchy problem | oral | We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study also a variant of the inverse problem of the Cauchy problem and prove that the considered inverse problem has a solution under certain regularity condition. We illustrate the Cauchy and the inverse problems in some interesting examples such that the families of the characteristic curves have either common envelopes or singular points. In these cases the definition domain of the solution of the differential equation contains a gap. | Abstracts of communications; http://www1.unipa.it/~giovanni.falcone/Participants2016.html |
| VII International Joint Conference of the Georgian Mathematical Union and Georgian Mechanical Union “Continuum Mechanics and Related Problems of Analysis ” | Batumi, Georgia | 2016 | 5-9 September | Georgian Mathematical Union, Georgian Mechanical Union, Batumi State University | The General Integrals of Quasi-linear equations and domains of propagation of the solutions of non-linear Cauchy Problems | oral | 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. | http://www.gmu.ge/Batumi2016/ |
| International Conference " Computer science and information technologies" | Erevan, Armenia | 2015 | 28 Sept.-2 Oct | "The National Academy of Science of Armenia The Institute for Informatics and Automation Problems" | Some properties of Hadamard Matrices | oral | One numerical characteristic of the Hadamard matrices is discussed. | http://ieeexplore.ieee.org/document/7358251/?reload=true http://ieeexplore.ieee.org/abstract/document/7358251/?reload=true https://csit.am/2015/ |
| International Conference " Computer science and information technologies" | Erevan, Armenia | 2015 | 28 Sept.-2 Oct | "The National Academy of Science of Armenia The Institute for Informatics and Automation Problems" | The Numerical Algorithm for the Quasi-linear Differential Equation of Mixed Type. | oral | 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. | https://csit.am/2015/ Book of Abstracts of the Conference - https://dl.acm.org/doi/proceedings/10.5555/2878961 |
| The International Scientific Conference Dedicated to Academician I.Prangishvili's 85th Anniversary "Information and Computer Technologies, Modelling, Control" | | 2015 | November 3-5 | Georgian Technical University, Shota Rustaveli national science foundation of Georgia | The Numerical Algorithm for the Quasi-linear Differential Equation of Mixed Type. | oral | 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. | http://www.ict-mc.gtu.ge/ http://www.ict-mc.gtu.ge/conference.pdf |
| VI International Conference of the Georgian Mathematical Union | | 2015 | July 12-16 | Georgian Mathematical Union | On the nonlinear analogue of the Darboux problem | oral | In this talk for the well-known nonlinear oscillation equation we consider a problem which is a nonlinear analogue of the Darboux problem and consists in the simultaneous definition of a solution and its regular propagation domain. The question of solvability of the formulated problem is solved by the method of characteristics. | http://gmu.gtu.ge/Batumi2015/ |
| Workshop "Lie Groups, Differential Equations and Geometry", July 31, 2015, Università degli Studi di Palermo, Dipartimento di Informatica e Matematica, Italy | Palermo, Italy | 2015 | July 22-31 | Eurocomission | On a functional inequality | oral | The proof of a functional inequality is presented | Abstracts of communications |
| Caucasian Mathematics Conference I | Tbilisi, Georgia | 2014 | September 5–6 | European Mathematical Society (EMS), Armenian, Azerbaijan, Georgian, and Turkish Mathematical Societies | On one mixed characteristic problem for a nonlinear oscillation equation | oral | Considered a mixed characteristic problem for a nonlinear oscillation equation. The structures of these domains up to the proximity of the points of degeneracy of degree of the equation are described. | https://euro-math-soc.eu/cmc/ http://www.mathnet.ru/php/conference.phtml?confid=575&option_lang=eng |
| V International conference of the Georgian Mathematical Union | Batumi, Georgia | 2014 | September 8–12 | Georgian Technical University, Batumi State University | | oral | Considered a mixed characteristic problem for a nonlinear oscillation equation. The structures of these domains up to the proximity of the points of degeneracy of degree of the equation are described. | http://www.gmu.ge/Batumi2014/ |
| International Conference “Lie Groups, Differential Equation and Geometry” | Batumi, Georgia | 2013 | June 10-22 | "Georgian Technical University, Batumi State University Georgian National Academy of Sciences, University of Debrecen, University of Palermo... " | On the Initial-Characteristic Problem for a Nonlinear Oscilation Equation | oral | Considered a nonlinear analogue of the characteristic Goursat problem for a nonlinear oscillation equation, which makes it possible to simultaneously define regular solutions and extension domains. The structures of these domains up to the proximity of the points of degeneracy of degree of the equation are described. | http://rmi.tsu.ge/mma/ http://rmi.tsu.ge/mma/program_Batumi_2013.pdf |
| International Conference “Lie Groups, Differential Equation and Geometry” | Batumi, Georgia | 2013 | June 10-22 | Georgian Technical University, Batumi State University | On a Variant of the Characteristic Problem | oral | One variant characteristic problem for the quasi-linear equation is studied. The theorem of the existence of a solution is proved. | Abstracts of communications |
| IV International conference of the Georgian Mathematical Union | Tbilisi-Batumi, Georgia | 2013 | September 9-15 | Georgian Mathematical Union | On a variant of a characteristic problem for the quasi-linear equation | oral | One nonlinear variant characteristic problem for the quasi-linear equation is studied. The theorem of the existence of a solution is proved. | http://gmu.gtu.ge/Batumi2013/index.html |
| III International Conference of the Georgian Mathematical Union | Batumi, Georgia | 2012 | September 2-9 | Georgian Technical University, Batumi State University | One nonlinear variant of the Darboux type nonlocal problem | oral | One nonlinear variant of the Darboux type nonlocal problem is studied. The theorem of the existence of a solution is proved | http://rmi.ge/~gmu/III_Annual_Conference/geo/confprogram/Conference2012.pdf |
| II International Conference Dedicated to the 70th Anniversary of the Georgian National Academy of Sciences&the 120th Birthday of its First President Academician Nikoloz Muskhelishvili, | Tbilisi, Georgia | 2011 | September 15-19 | Georgian Mathematical Union | On the Domains of Propagation of Characteristic Curves of Non-Strictly Hyperbolic Equations | oral | Domains of propagation of curves characteristic of non-strictly hyperbolic equations are studied. | http://www.rmi.ge/~gmu/II_Annual_Conference/comming/Program_Batumi_2011_Final.pdf |
| International Conference "Modern Algebra and its applications" | Batumi, Georgia | 2011 | September 19-25, 2011 | Batumi State University | The Cauchy Problem for quasi-linear hyperbolic equation with closed support of data. | oral | 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. | - |
| Ilia Vekua Institute of Applied Mathematics of Iv. Javakhishvili State University | Tbilisi, Georgia | 2010 | 21-23 April | Ilia Vekua Institute of Applied Mathematics of Iv. Javakhishvili State University | On the Domains of Propagation of Waves Determined by Perturbations on the Closed Support | oral | 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. | http://www.viam.science.tsu.ge/geo/enlrg |
| International Conference “Information and Computational Technologies” dedicated to commemoration of Professors Elene Dekanosidze and Murman Tsuladze | Tbilisi, Georgia | 2010 | 2-6 May | N. Muskhelishvili Institute of Computational Mathematics and St. Andrew the First Called Georgian University of the Patriarchy of Georgia | On non-local problems for Quasi-linear hyperbolic equations | oral | For one quasi-linear partial differential equation a version of non-local Problem is considered. The problem is solved by using of characteristic invariants. | http://micm.edu.ge/wp-content/uploads/2020/06/Abstracts_CONF_MICM_2010.pdf |
| The International Scientific Conference "Information and Computer Technologies, Modeling, Control" | Tbilisi, Georgia | 2010 | October 2-4 | Georgian Technical University, Institute of Control Sciences of RAS, Graz University of Technology, EASA... | On Modeling of Process of Formation of Impenetrable Domains for Non-linear Waves | oral | For one class of quasi-linear partial differential equation a non-linear version of Cauchy Problem is considered. | http://gesj.internet-academy.org.ge/conf/en/program_en.php?conf= |
| Ukrainian Mathematical Congress − 2009 (Dedicated to the Centennial of Nikolai N. Bogoliubov) | Kiev, Ukraine | 2009 | August 27−29 | Institute of Mathematics of NASU | On Quiet Zones in Nonlinear Wave Propagation Regions | oral | The structure of the characteristic areas of the mixed type equation is studied. | https://www.imath.kiev.ua/~congress2009/partUMC2009.html |
| Ukrainian Mathematical Congress − 2009 (Dedicated to the Centennial of Nikolai N. Bogoliubov) | Kiev, Ukraine | 2009 | August 27−29 | Institute of Mathematics of NASU | On Quiet Zones in Nonlinear Wave Propagation Regions | oral | The structure of the characteristic areas of the mixed type equation is studied. | https://www.imath.kiev.ua/~congress2009/partUMC2009.html |
| International Conference on Modern Problems in Applied Mathematics Dedicated to the 90 Anniversary of the Iv. Javakhishvili Tbilisi State University & 40 Anniversary of the I. Vekua Institute of Applied Mathematics. | Tbilisi, Georgia | 2008 | 7-9 ოქტომბერი | I. Vekua Institute of Applied Math., Tbilisi State University | Some non-classical problems for quasi-linear equation | oral | For the quasi-linear mixed second order equation the two problems are studied. The existence and uniqueness theorems of the solutions of the considered problems are given. | http://www.viam.science.tsu.ge/files/viam40/tezisebis_krebuli.pdf |
| XXII Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics | Tbilisi, Georgia | 2008 | 22-24 April | I. Vekua Institute of Applied Math. | Nonclassical Problems for Second-Order Mixed Type Partial Differencial Equation | oral | For one second-order mixed-type equation, the non-classical problems of the Goursat and Darbus types are studied. | http://www.viam.science.tsu.ge/eng/enlrg |
| Enlarged Session of the Seminar of I. Vekua Institute of Applied Mathematics | Tbilisi, Georgia | 2006 | 20-22 აპრილი | I. Vekua Institute of Applied Math. | On numerical solution of the boundary value problem for uniform equilibtrium equations for non-shallow shells | oral | The system of the equilibrium equations of the non-shallow (with changing internal geometry on thickness) spherical bodies of shell type are discussed, when the displacement vector is independent from the thickness coordinate. the boundary value problem with the help of the method of finite difference, for the rectangular area, for non-shallow spherical shells has been solved.
| http://www.viam.science.tsu.ge/enl_ses/vol21/vol21.htm |
