[书籍] 对称方法在偏微分方程中的应用
出版社:
世界图书出版公司
简介:
This book is a sequel to Symmetries and Integration Methods (2002), by George W. Bluman and Stephen C. Anco. It includes a significant update of the material in the last three chapters of Symmet'ries an,d Dzjjerential Equa-tions (1989; reprinted with corrections, 1996), by George W. Bluman and Sukeyuki Kumei. The emphasis in the present book is on how to find sys-tematically symmetries (local and nonlocal) and conservation laws (local and nonlocal) of a given PDE system and how to use systematically symmetries and conservation laws for related applications. In particular, for a given PDE system, it is shown how systematically (1) to find higher-order and nonlocal symmetries of the system; (2) to construct by direct methods its conserva- tion laws through finding sets of conservation law multipliers and formulas to obtain the fluxes of a conservation law from a known set of multipliers; (3) to determine whether it has a linearization by an invertible mapping and con- struct such a linearization when one exists from knowledge of its symmetries andlor conservation law multipliers, in the case wheii the given PDE system is nonlinear; (4) to use conservation laws to construct equivalent nonlocally related systems; (5) to use such nonlocally related systems to obtain nonlo- cal symmetries, nonlocal conservation laws and non-invertible mappings to linear systems; and (6) to construct specific solutions from reductions arising from its symmetries as well as from extensions of symmetry methods to find such reductions. This book is aimed at applied mathematicians; scientists and engineers interested in finding solutions of partial differential equations and is written in the style of the above-mentioned 1989 book by Bluman and Kumei. There are numerous examples involving various well-known physical and engineering PDE systems.
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