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Titlebook: Introduction to Nonlinear Dispersive Equations; Felipe Linares,Gustavo Ponce Textbook 2015Latest edition Springer-Verlag New York 2015 Kor

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書目名稱Introduction to Nonlinear Dispersive Equations
編輯Felipe Linares,Gustavo Ponce
視頻videohttp://file.papertrans.cn/474/473964/473964.mp4
概述Includes a nice selection of topics.Contains a large section of non-standard exercises.Offers accessible presentation of key tools in harmonic and Fourier analysis.Includes supplementary material:
叢書名稱Universitext
圖書封面Titlebook: Introduction to Nonlinear Dispersive Equations;  Felipe Linares,Gustavo Ponce Textbook 2015Latest edition Springer-Verlag New York 2015 Kor
描述.This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schr?dinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schr?dinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schr?dinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schr?dinger equation, taking the reader to the forefront of recent research..Thesecond edition of .Introduction to Nonlinear Dispersive Equations. builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercis
出版日期Textbook 2015Latest edition
關(guān)鍵詞Korteweg-de Vries Equation; Marcinkiewicz interpolation theorem; Riesz–Thorin convexity theorem; Stein
版次2
doihttps://doi.org/10.1007/978-1-4939-2181-2
isbn_softcover978-1-4939-2180-5
isbn_ebook978-1-4939-2181-2Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag New York 2015
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,The Nonlinear Schr?dinger Equation: Local Theory,In this chapter, we shall study local well-posedness of the nonlinear initial value problem (IVP) associated to the Schr?dinger equation. We discuss results for data in ., ., and other well-posedness issues. We end the chapter with some remarks and comments regarding the issues discussed in the previous sections.
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Asymptotic Behavior of Solutions for the k-gKdV Equations,This chapter is concerned with the longtime behavior of solutions to the initial value problem (IVP) associated to the k-generalized Korteweg-de Vries (k-gKdV) equations. We shall restrict ourselves to consider only real solutions of the associated IVP. We will discuss global well-posedness results as well as some blow-up results.
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The Fourier Transform,case . is considered in Section?1.2. The space of tempered distributions is briefly considered in Section?1.3. Finally, Sections?1.4 and 1.5 give an introduction to the study of oscillatory integrals in one dimension and some applications, respectively.
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