Nonlinear wave equations

by Kichenassamy, Satyanad

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Title Statements

Full title :Nonlinear wave equations / Satyanad Kichenassamy.

Summary

This up-to-date reference/text examines the mathematical aspects of nonlinear wave propagation - emphasizing nonlinear hyperbolic problems - and introduces the most effective tools for the study of perturbation methods and for exploring global existence, singularity formation, and large-time behavior of solutions. Containing key bibliographic citations, Nonlinear Wave Equations is an excellent reference for mathematical analysts and industrial and applied mathematicians; electrical and electronics, aerospace, mechanical, control, systems, and computer engineers; and physicists; as well as an invaluable text for graduate-level students in these disciplines with an understanding of partial differential equations.

Edition Statements

Publication Date:©1996.

Publication Statements

Publisher(s):M. Dekker
Place of Publication:New York
Language:eng
Publication Date:©1996.

The Physical Object

Description:1 online resource.

Edition Identifiers

ISBN:9781000447453, 1000447456
oclc:on1251511632
LC Classification:QA927
Dewey Decimal:531/.1133/01515355

1. Linear Wave Propagation. 1.1. The Fourier transform. 1.2. The Sobolev inequality. 1.3. The initial-value problem. 1.4. Decay estimates. 1.5. Propagation of singularities. 1.6. What is a wave? -- 2. Local and Global Existence. 2.1. The analytic Cauchy problem. 2.2. The energy method. 2.3. Semi-group techniques. 2.4. Global existence for small data. 2.5. Other iteration techniques -- 3. Singularity Formation. 3.1. Criteria for breakdown. 3.2. Propagation of weak singularities. 3.3. Shock waves. 3.4. Models for singularity formation -- 4. Solitons and Inverse Scattering. 4.1. Universal equations. 4.2. Isospectrality. 4.3. The Korteweg-de Vries equation. 4.4. The AKNS systems. 4.5. Riemann-Hilbert and [theta] formulations. 4.6. Criteria for integrability -- 5. Perturbation Methods. 5.1. Perturbation of spectra. 5.2. Implicit function theorems. 5.3. Nonlinear geometrical optics. 5.4. Whitham's theory. 5.5. Soliton perturbation. 5.6. Application of invariant manifold theory -- 6. General Relativity. 6.1. Preliminaries. 6.2. Einstein's equations. 6.3. The Cauchy problem. 6.4. Linearization stability and perturbations. 6.5. Singularities and cosmic censorship. 6.6. Exact solutions