Symmetry Problems. The Navier–Stokes Problem.
Morgan & Claypool Publishers (Verlag)
978-1-68173-505-4 (ISBN)
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This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier—Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier—Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.
Alexander G. Ramm, Ph.D., was born in Russia, immigrated to the U.S. in 1979, and is a U.S. citizen. He is Professor of Mathematics with broad interests in analysis, scattering theory, inverse problems, theoretical physics, engineering, signal estimation, tomography, theoretical numerical analysis, and applied mathematics. He is an author of 690 research papers, 16 monographs, and an editor of 3 books. He has lectured in many universities throughout the world, presented approximately 150 invited and plenary talks at various conferences, and has supervised 11 Ph.D. students. He was Fulbright Research Professor in Israel and in Ukraine, distinguished visiting professor in Mexico and Egypt, Mercator professor, invited plenary speaker at the 7th PACOM, won the Khwarizmi international award, and received other honors. Recently he solved inverse scattering problems with non-over-determined data and the many-body wavescattering problem when the scatterers are small particles of an arbitrary shape; Dr. Ramm used this theory to give a recipe for creating materials with a desired refraction coefficient, gave a solution to the refined Pompeiu problem and proved the refined Schiffer's conjecture. Steven G. Krantz, Washington University, St. Louis.
Preface
Introduction
Necessary and Sufficient Conditions for a Scatterer to be Spherically Symmetric
Symmetry Problems for the Helmholtz Equation
Other Symmetry Problems
Solution to the Navier--Stokes Problem
Inverse Problem of Potential Theory
Bibliography
Author's Biography
| Erscheinungsdatum | 18.03.2019 |
|---|---|
| Reihe/Serie | Synthesis Lectures on Mathematics and Statistics |
| Mitarbeit |
Herausgeber (Serie): Steven G. Krantz |
| Verlagsort | San Rafael |
| Sprache | englisch |
| Maße | 191 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| ISBN-10 | 1-68173-505-9 / 1681735059 |
| ISBN-13 | 978-1-68173-505-4 / 9781681735054 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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