| 书目名称 | Methods for Partial Differential Equations | | 副标题 | Qualitative Properti | | 编辑 | Marcelo R. Ebert,Michael Reissig | | 视频video | | | 概述 | Provides an overview on different topics of the theory of partial differential equations.Presents a comprehensive treatment of semilinear models by using appropriate qualitative properties and a-prior | | 图书封面 |  | | 描述 | .This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area..The book is organized in five parts:.In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren‘s uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger‘s equation..Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes Laplace equation, heat equation and wave equation as well as the different features of each theory. It also discusses the notion of energy of solutions, a highly effective tool f | | 出版日期 | Textbook 2018 | | 关键词 | well-posedness of mixed problems and Cauchy problems; regularity results; potential theory; energy meth | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-66456-9 | | isbn_softcover | 978-3-030-09772-1 | | isbn_ebook | 978-3-319-66456-9 | | copyright | Springer International Publishing AG 2018 |
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