Plenary Lecture

Direct and Time Reverse Problems for Hyperbolic Heat Equation -  New Models for Intensive Steel Quenching Processes



Professor Andris Buikis
Institute of Mathematics and Computer Science
University of Latvia
Raina bulv. 29, Riga, LV1459
LATVIA

Email: buikis@latnet.lv

Abstract: Intensive quenching processes are important branches of modern metallurgical technologies. In new ecologically clean steel quenching processes important aspect is the heat exchange with the surrounding cold water. But the type of heat exchange is mostly defined by initial heat flux densities: if initial heat flux density is higher as first critical heat flux density, then the full film boiling is observed. If the initial heat flux density is lower, then the nucleate boiling establishes on the sample’s surface. This is the preferable type of heat exchange process, because it provides the intensity of the process and defines the quality of the obtained material. In 2005 we proposed the hyperbolic heat equation as mathematical model for intensive steel quenching process. In several papers during 2005-2008 we have developed some approaches (Green function method, original conservative averaging method) for the solving of ill-posed time reverse problems for the parabolic part of the hyperbolic heat equation. These ideas gave quite good compatibility of theoretical and experimental initial heat flux densities.
In this lecture we develop some new ideas for the solving of time reverse problems for the hyperbolic heat equation. They lead us to well-posed statements for determination of initial heat fluxes instead of ill-posed statements as it was in our previous papers.

 

Brief Biography of the Speaker:

Professor Andris BUIKIS

• Professor, University of Latvia, Faculty of Physics and Mathematics, Department of Mathematics

• Head of Laboratory of Mathematical Technologies, Institute of Mathematics and Computer Science, University of Latvia
   

Born: March 15, 1939, Valka, Latvia
 

Interests:

•  Mathematical Modelling

•  Mathematical Problems of Heat and Mass Transfer, Especially for Layered Media

• Analytical and Numerical Methods for Partial Differential Equations

• Innovative Energetic

• Philosophy of Science

Languages: German, English, Latvian, Russian

Education:

• University of Latvia (Faculty of Physics and Mathematics), 1963

• Dr.math. (Candidate of Science in former USSR), University of Latvia, 1970

• Dr.habil.math. (Doctor of Science in former USSR), University of Kasan, Russia, 1988

• Professor, University of Latvia, 1991

Experience:

• Junior Researcher, Senior Researcher, Computing Centre, University of Latvia, 1962 - 1972

• Assistant Professor and Head of Chair of Applied Mathematics, Faculty of Physics and Mathematics, University of Latvia, 1972 - 1976

• Assistant Professor and Head of Chair of Differential Equations and Numerical Methods, Faculty of Physics and Mathematics, University of Latvia, 1976 - 1984

• Senior Researcher, Faculty of Physics and Mathematics, University of Latvia, 1984 - 1986

• Assistant Professor, Chair of Differential Equations and Numerical Methods, Faculty of Physics and Mathematics, University of Latvia, 1986 - 1988

• Senior Researcher, Head of Laboratory of Mathematical Physics, Institute of Physics, Latvian Academy of Sciences, 1988 - 1991

• Director, Institute of Mathematics, Latvian Academy of Sciences and Latvian University, 1991 - 1996; 2003 - 2006

• Head of Laboratory of Mathematical Physics (1996 -2006 ) and Head of Scientific Council (1996 – 2003), Institute of Mathematics, Latvian Academy of Sciences and Latvian University

• Director, Science and Dialogue Centre of Latvia, 1993 -2007

• Head of Laboratory of Mathematical Technologies (2006-), Institute of Mathematics and Computer Science, University of Latvia

Honours and Awards:

• Corresponding Member, Latvian Academy of Sciences, 1992 - 1997

• Full Member, Latvian Academy of Sciences, 1997

• The Latvian Academy of Sciences Piers Bohl Prize for a cycle of papers “Method of Conservative Averaging, Theory and Applications”, 2005

• Member of Board, Soros Foundation - Latvia, 1997

• Head of "Spidola" Council, Culture Foundation of Latvia, 1987 - 1992

• Member of Board, Vidzemes University College, 1996 - 1998

Professional Activties and Memberships:

• Member, Senate of the Latvian Academy of Sciences, 1994 -

• Member, Vidzeme University College Advisory Board, 1997-2002

• Vice-Chairman (in Mathematics), Latvian Council of Science Expert Committee on "Physics, Mathematics & Astronomy", 1991 - 1993

• Chairman, Promotion Council for Mathematics, 1992 -

• Member, Editorial Advisory Board for Proceedings of the Latvian Academy of Sciences, 1988-1995

• Member, Editorial Advisory Board for Computational Methods in Applied Mathematics, 2000-

• Member of Editorial Advisory Board, Journal Mathematical Modelling and Analysis (The Baltic Journal on Mathematical Applications, Numerical Analysis and Differential Equations), Lithuania, 1999-

• Editor, Progress in Industrial Mathematics at ECMI 2002 , Springer

• Member, Editorial Board for International Journal of Applied Mathematical Sciences (IJAMS), 2004 -

• Member, Gesellschaft Angewandte Matematik und Mechanik, Germany 1991 -

• Member, International Sociological Association, 1998-2002

• Holder of state capital share at The Latvian Institute, 1998 -2004

• Member, American Mathematical Society, 1999 –

• Member, World Scientific and Engineering Academy and Society, 2006-