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Titlebook: Nonlinear Wave Equations; Tatsien Li,Yi Zhou Book 2017 Springer-Verlag GmbH Germany and Shanghai Scientific and Technical Publishers 2017

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發(fā)表于 2025-3-21 16:52:46 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Nonlinear Wave Equations
編輯Tatsien Li,Yi Zhou
視頻videohttp://file.papertrans.cn/668/667748/667748.mp4
概述Establishes the complete lower bound estimates of lifespan for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions.Proposes t
叢書名稱Series in Contemporary Mathematics
圖書封面Titlebook: Nonlinear Wave Equations;  Tatsien Li,Yi Zhou Book 2017 Springer-Verlag GmbH Germany and Shanghai Scientific and Technical Publishers 2017
描述.This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms.. .Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut.ions to the corresponding linear problems, the method simply applies the contraction mapping principle..
出版日期Book 2017
關鍵詞Cauchy problem; asymptotic stability; blow-up phenomenon; global iteration method; lower bound estimates
版次1
doihttps://doi.org/10.1007/978-3-662-55725-9
isbn_softcover978-3-662-57250-4
isbn_ebook978-3-662-55725-9Series ISSN 2364-009X Series E-ISSN 2364-0103
issn_series 2364-009X
copyrightSpringer-Verlag GmbH Germany and Shanghai Scientific and Technical Publishers 2017
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Introduction and Overview,. are a kind of important infinite-dimensional dynamical systems. The so-called infinite-dimensional dynamical system is a system described by nonlinear evolutionary partial differential equations (nonlinear evolutionary equations for short).
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Linear Wave Equations,In this section we consider the following Cauchy problem of linear wave equations ..
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Sobolev Type Inequalities with Decay Factor,In this chapter we are going to establish Sobolev type inequalities with decay factor. The key point is to consider the Lorentz invariance of the wave operator and then introduce a group of first-order partial differential operators instead of the normal differential operators in the differential operations (see Klainerman 1985).
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Cauchy Problem of the Second-Order Linear Hyperbolic Equations,In order to solve the Cauchy problem of nonlinear wave equations later (see Chap.?.), we will consider in this chapter the following Cauchy problem of .-dimensional linear hyperbolic equations.
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