This book presents the analysis of viscous flows in thin tube structures, and develops a multi-scale method for modeling blood flow. For the readers convenience, the authors introduce all necessary notions and theorems from functional analysis and the classical theory of the Navier-Stokes equations. The problems of all asymptotic methods used in the book are explained as well, such as the dimension reduction and the boundary layer method. Through several numerical experiments, readers will discover that the proposed methods are more flexible than the theoretically predicted conditions. Multiscale Analysis of Viscous Flows in Thin Tube Structures will be a valuable resource for a wide range of readers, including applied mathematicians, specialists in bio-engineering, and biophysicists.
Preface.- Introduction.- Preliminaries.- Poiseuille Flows.- Stokes
Problem and Stokes Operator.- Steady-State Stokes and NavierStokes Equations
in Tube Structures.- Nonstationary NavierStokes Equations.- Time-Periodic
Case.- Bibliographical Remarks.- Bibliography.- Index.
Grigory Panassenko is a Chief Researcher at Vilnius University. He was Distinguished Professor at University Jean Monnet (Saint-Etienne, France) until 2023. He graduated from Moscow State University M.V. Lomonosov in 1976 where he was sequentially Ph.D.student (supervisor Prof. N.S.Bakhvalov), Associate Professor, and Professor. In 1993, he began working as Professor at the University Jean Monnet, where from 2004 until 2011 he was head of laboratory, and from 2011 until 2023 head of research federation. From 2018 he participates in research projects of Vilnius University. Professor Panasenko is the author of 4 books and 160 articles in applied mathematics. From 2023 he is Editor-in-Chief of Applicable Analysis journal. Award: Medal for the young researcher of the USSR Academy of Sciences (1986). Konstantin Pileckas got his Ph.D. in mathematics from the Leningrad Branch of Steklov Mathematical Institute (LOMI), Russia, under the supervision of Prof. V. A. Solonnikov in 1982. In 1994 he received a habilitation from the University of Paderborn, Germany. In the period of 1982-1990, K. Pileckas worked as a research fellow at the Institute of Mathematics and Informatics in Vilnius. From 1990-1991 he was A. von Humboldt Fellow at the University of Paderborn and from 1991 until 1996 he did research there. In 1996 he returned to Lithuania and continued his research work at the Institute of Mathematics and Informatics, where from 1997 until 2008 he was head of the Department of Differential Equations. At the same time, K. Pileckas got the professor position at Vilnius University, one of the oldest universities in Eastern and Central Europe. Since 2008 he is head of the Department of Differential Equations at Vilnius University.
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