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Prof. Akif Ibragimov
Texas Tech University, Lubbock, Texas US., USA
Qualitative properties of the non-linear equations in porous media and application in engineering
In this lecture we will focus on the analysis of properties of the solution of non-linear equations in porous media and some engineering applications.  

It has been observed for many years that the traditional linear Darcy equation does not adequately predict many important features of gas and liquid flows in the reservoir. Essentially, modern challenges in reservoir engineering introduced a new class of mathematical problems using machinery of partial differential equations. We will discuss the discovery of novel relations between main hydrodynamic parameters of the flows in porous media and corresponding properties of the solution of degenerate parabolic equations.  The study of a class of generalized non-linear momentum equation, covering pre-Darcy, Darcy and post-Darcy equations within one framework of models based on non-linear parabolic equations of second order, will be introduced. 

We will also discuss qualitative properties of the solution of the corresponding equations and the relation of these theoretical results to practical engineering applications. 

In our talk we will also address some unsolved important problems closely related to modern technology that has a potential to increase significantly oil and gas recoverable reserves.
Akif Ibragimov received his PhD from the Moscow State University, and Doctor of Science degree from Steklov Institute of Mathematics in Moscow. He is currently Professor at Texas Tech University, Department of Mathematics and Statistics, and also served as Visiting Professor at Texas A&M University, and Senior Research Scientist with Knowledge Based Systems, Inc. Before coming to the US he was a Senior Reservoir Specialist with BP Amoco-Azerbaijan, and Professor at the Gubkin Russian State University of Oil and Gas in Moscow. Prior to embarking on applied research in Oil and Gas industry, Akif Ibragimov was Visiting Researcher atSteklov Institute of Mathematics, and at the Moscow State University. He was also served as the head of the Department of Partial Differential Equation in Azerbaijan Academy of Science. Akif Ibragimov belongs to the school of qualitative theory of PDEestablished by Landis and Kondratiev at the Moscow State University. His adviser and teacher Evgeniy Mikhailovich Landis is one of the most influential mathematicians in the area of Qualitative Theory of PDE.From 1988 Akif Ibragimov was actively involved in developing semi-analytical methods for solution of the equations in porous media and their application in reservoir engineering. After moving to USA he worked in different areas of industrial mathematics including image processing, data mining, and modeling off electrochemical processes.  From 2002 he also worked in the area of modeling and analyses of the new models of the biomedical processes. Recently he established a new approach to solving engineering problems arising in oil and gas industry using machinery of non-linear PDE. Akif Ibragimov published more than 100 papers spanning the theory of PDE to different industrial and applied problems in biochemistry, biomedicine, image processes and porous media.

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