Mathematical Models in Boundary Layer Theory (Applied Mathematics) 1st Edition by V.N. Samokhin (PDF)

Description

Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory.Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution. Written by the world’s foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory’s importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The mathematical theory of boundary layers is the study of the Prandtl system of partial differential equations. Olga Oleinik and her pupils (the second author Samokhin is one of them) contributed in an essential way to this topic, and their contributions as well as the results obtained by other researchers fill this volume. Written only two years before Oleinik’s death, the style is conversational but fully rigorous. The result is a monograph that gives the reader the feel of the richness of a field where many important open problems are still unsolved, but also the wealth of results proper of an handbook on the topic. It would be not possible to describe precisely the contents within the space reserved for the present reviews, but however it should be noted that a chapter is devoted to the finite difference approximation of boundary layers, and that two chapters are devoted to non mainstream topics in the field, precisely to boundary layers in non-Newtonian fluids and in Magnetohydrodynamics. The production is superb as it used to be for the C&H monographs in this series: in the end, to put it simply, it has no weak points.

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