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This book presents the analysis of viscous flows in thin tube structures, and develops a multi-scale method for modeling blood flow. For the reader’s 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.
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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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