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<body stylesrc="proba.html" background="Lavender_Design204.gif" bgcolor="#FFFFFF" text="#000080">  <p align="center"><a name="Sobolev Institute of Mathematics, Novosibirsk, Russia"><font color="#008080" size="5"><em>Sobolev Institute of Mathematics, Novosibirsk, Russia</em></font></a></p> <p align="center"><font color="#008080"><strong>Head of Laboratory:</strong></font> <a href="romanov1.html"><strong>Prof. V.G. Romanov</strong></a></p> <p align="center"><a name="Research Activities"><font color="#FF00FF" size="5"><strong>Research Activities</strong></font></a></p> <blockquote> <blockquote> <p align="left"><font size="4">Central subject of investigations is inverse problems connected to differential equations describing the process of wave propagation (acoustic, elastic, electromagnetic and so on). Inverse problems consist in determination of variable coefficients of differential equations using information about the solution of these equations. As a rule, this information is given on the boundary of some domain inside which the coefficients are to be found. The investigation techniques of inverse problems include, certainly, as a necessary part, a comprehensive investigation of initial boundary value problems. The latter problems usually are called direct problems.</font></p> </blockquote> </blockquote> <p align="center"><font color="#FF00FF" size="4"><strong>Main areas of research:</strong></font></p> <ol> <li><p align="left"><font size="4">Investigation of uniqueness, stability and existence of inverse problems for equations and systems of hyperbolic type including acoustic, elastic, electrodynamic and electroelastic equations.</font></p> </li> <li><p align="left"><font size="4">Construction and justification of numerical methods for solving inverse problems. These methods include extension of the solution from the boundary of the domain, minimization of a residual functional using conjugate gradients, discrete analogs of Gelfand-Levitan equation.</font></p> </li> <li><p align="left"><font size="4">Development of integral geometry (tomography) methods as applied to inverse problems for elastic and electrodynamic equations (inverse kinematic problem in linear and nonlinear variants, ray setting of inverse problems).</font></p> </li> <li><p align="left"><font size="4">Development of tomographic methods based on transport equation taking into consideration absorption and scattering. Obtaining stability theorems and creating numerical algorithms.</font></p> </li> <li><p align="left"><font size="4">Mathematical modeling of geophysical problems for inhomogeneous media.</font></p> </li> </ol> <div align="center"><center> <table border="0" cellspacing="30" width="100%"> <tr> <td width="33%"><font size="4"><a href="#Research Activities"><img src="Dark_Blue_Beveled2194.gif" border="0" WIDTH="32" HEIGHT="25"></a><br> Previous</font></td> <td width="33%"><font size="4"><a href="#People"><img src="Dark_Blue_Beveled2194.gif" border="0" WIDTH="32" HEIGHT="25"></a><br> Next</font></td> <td width="34%"><font size="4"><a href="#Sobolev Institute of Mathematics, Novosibirsk, Russia"><img src="Dark_Blue_Beveled2194.gif" border="0" WIDTH="32" HEIGHT="25"></a><br> Top</font></td> </tr> </table> </center></div> <hr> <p align="center"><font color="#FF00FF" size="5"><strong><img src="Mail90B1.gif" WIDTH="32" HEIGHT="32"><a name="Contact Information">Contact Information</a></strong></font></p> <div align="center"><center> <table border="0" cellspacing="30" width="100%"> <tr> <td width="50%">Postal address:<br> Sobolev Institute of Mathematics<br> 630090, Novosibirsk 90,<br> Acad. Koptyug's Avenue, 4<br> Russia</td> <td width="50%">Fax: 007-3832-33-25-98<br> Tel.: 007-3832-332-987,<br> 007-3832-33-35-45<br> E-mail: <a href="mailto:romanov@math.nsc.ru">romanov@math.nsc.ru</a></td> </tr> </table> </center></div> <p><font size="4">Dr. A.N. Bondarenko </font><a href="mailto:bondar@math.nsc.ru">bondar@math.nsc.ru</a><font size="4"><br> Dr. T.V. Bugueva </font><a href="mailto:bugueva@math.nsc.ru">bugueva@math.nsc.ru</a><font size="4"><br> Prof. S.I. Kabanikhin </font><a href="mailto:kabanikh@math.nsc.ru">kabanikh@math.nsc.ru</a><font size="4"><br> Dr. A.L. Karchevsky </font><a href="mailto:karchevs@math.nsc.ru">karchevs@math.nsc.ru</a><font size="4"><br> Dr. O.A. Klimenko </font><a href="mailto:klimenko@math.nsc.ru">klimenko@math.nsc.ru</a><font size="4"><br> Dr. S.V. Martakov </font><a href="mailto:martakov@math.nsc.ru">martakov@math.nsc.ru</a><font size="4"><br> Dr. R.G. Mukhometov <br> Dr. V.I. Priimenko</font> <a href="mailto:slava@cana.lenep.uenf.br">slava@cana.lenep.uenf.br</a><br> <font size="4">Prof. V.G. Romanov </font><a href="mailto:romanov@math.nsc.ru">romanov@math.nsc.ru</a><font size="4"><br> Dr. M.V. Soukhoroslova </font><font size="3"><a href="mailto:soukh@math.nsc.ru">soukh@math.nsc.ru</a><br> </font><font size="4">Prof. V.G. Yakhno </font><a href="mailto:yakhno@math.nsc.ru">yakhno@math.nsc.ru</a><br> </p> <p> </p> <p> </p> <hr> <p align="center"><font color="#FF00FF" size="5"><strong><img src="Pencil_and_Paper6153.gif" WIDTH="20" HEIGHT="18"><a name="Seminar of Laboratory of Wave Process">Seminar </a></strong></font></p> <p align="left"><font size="4">Seminars usually take place on Friday afternoons at 4 p.m. in Rm. 417, Institute of Mathematics. All welcome ! </font></p> <p align="left"><font size="4">Please contact Olga Klimenko for further information, e-mail: <a href="mailto:klimenko@math.nsc.ru">klimenko@math.nsc.ru</a><br> tel.: 332-987</font></p> <hr> <p align="center"><font color="#FF00FF" size="5"><strong><img src="People7275.gif" WIDTH="20" HEIGHT="19"><a name="People">People</a></strong></font></p> <p align="left"><font size="4">Dr. A.N. Bondarenko <br> <a href="tania1.html">Dr. T.V. Bugueva </a><br> <a href="kabser.html">Prof. S.I. Kabanikhin </a><br> <a href="andrey1.html">Dr. A.L. Karchevsky </a><br> <a href="klimenko.htm">Dr. O.A. Klimenko </a><br> Dr. S.V. Martakov <br> Dr. R.G. Mukhometov <br> Dr. V.I. Priimenko <br> <a href="romanov1.html">Prof. V.G. Romanov <br> </a><a href="marina1.html">Dr. M.V. Soukhoroslova</a><br> <a href="yakhno.html">Prof. V.G. Yakhno </a></font></p> <div align="center"><center> <table border="0" cellspacing="30" width="100%"> <tr> <td width="33%"><font size="4"><a href="#Contact Information"><img src="Dark_Blue_Beveled2194.gif" border="0" WIDTH="32" HEIGHT="25"></a><br> Previous</font></td> <td width="33%"><font size="4"><a href="#Sobolev Institute of Mathematics, Novosibirsk, Russia"><img src="Dark_Blue_Beveled2194.gif" border="0" WIDTH="32" HEIGHT="25"></a><br> Top</font></td> <td width="34%"></td> </tr> </table> </center></div> <hr> <p><font size="2">Webmaster: <a href="mailto:klimenko@math.nsc.ru">klimenko@math.nsc.ru</a><br> Update: 18 Октябрь, 2001</font></p>  </body>