Global well -posedness for systems of nonlinear wave equations

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" Global well -posedness for systems of nonlinear wave equations "
Sawanya Sakuntasathien M. A. Rammaha

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	54324
Doc. No	:	TL24278
Call number	:	‭3297658‬
Main Entry	:	Sawanya Sakuntasathien
Title & Author	:	Global well -posedness for systems of nonlinear wave equations\ Sawanya Sakuntasathien
College	:	The University of Nebraska - Lincoln
Date	:	2008
Degree	:	Ph.D.
student score	:	2008
Page No	:	124
Abstract	:	This dissertation deals with the global well-posedness of the system of nonlinear wave equations [special characters omitted]in a bounded domain Ω ⊂ [special characters omitted], n = 1, 2, 3; with Dirichlét boundary conditions. The nonlinearities f1(u, v) and f2(u, v) act as a strong source in the system and the exponents of velocities are restricted to the range 0 < m, r ≤ 1. The non-critical case 0 < m, r < 1 and the critical case m = r = 1 are analyzed in Chapter 2 and Chapter 3, respectively. Under some restrictions on the parameters in the system we obtain several results on the existence of local solutions, global solutions, and uniqueness. In addition, we prove that weak solutions to the system blow up in finite time whenever the initial energy is negative and the exponent the source term is more dominant than the exponents of both damping terms.
Subject	:	Pure sciences; Nonlinear wave equations; PDEs; Well-posedness; Mathematics; 0405:Mathematics
Added Entry	:	M. A. Rammaha
Added Entry	:	The University of Nebraska - Lincoln