Global Propagation of Regular Nonlinear Hyperbolic Waves

Tatsien Li ()
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Tatsien Li: Fudan University, Department of Mathematics

A chapter in Recent Progress in Computational and Applied PDES, 2002, pp 243-258 from Springer

Abstract: Abstract In this work we shall consider the nonlinear hyperbolic waves described by the following Cauchy problem for first order quasilinear hyperbolic systems 1,2 $$ \left\{ \matrix{ {{\partial u} \over {\partial t}} + {\rm A}\left( u \right){{\partial u} \over {\partial x}} = 0, \hfill \cr t = 0:u = \varphi \left( x \right), \hfill \cr} \right. $$ where u = (u 1, ... ,u n ) T is the unknown vector function of (t,x), A(u) = (a ij (u))is an n × n matrix with suitably smoothentrics a ij (u) (i, j =1, ... ,n) and φ(x) = (φ 1(x), ... , φ n (x)) T is a C 1 vector function of x with bounded C 1norm.

Keywords: Cauchy Problem; Hyperbolic System; Null Condition; Small Initial Data; Quasilinear Hyperbolic System (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-0113-8_18

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DOI: 10.1007/978-1-4615-0113-8_18

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