Global Propagation of Regular Nonlinear Hyperbolic Waves
Global Propagation of Regular Nonlinear Hyperbolic Waves
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DOI：
10.1007/978-1-4615-0113-8_18
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发表时间：
2002-11
期刊：
影响因子：
--
通讯作者：
Tatsien Li;Libin Wang
中科院分区：
文献类型：
--
作者：
Tatsien Li;Libin Wang
In this work we shall consider the nonlinear hyperbolic waves described by the following Cauchy problem for first order quasilinear hyperbolic systems $$ \left\{ \matrix{ {{\partial u} \over {\partial t}} + {\rm A}\left( u \right){{\partial u} \over {\partial x}} = 0, \hfill \cr t = 0:u = \varphi \left( x \right), \hfill \cr} \right. $$ whereu= (u1, ... ,un)Tis the unknown vector function of (t,x),A(u) = (aij(u))is ann×nmatrix with suitably smoothentricsaij(u) (i,j=1, ... ,n) andφ(x) = (φ1(x), ... ,φn(x))Tis aC1vector function ofxwith boundedC1norm.
In this work we shall consider the nonlinear hyperbolic waves described by the following Cauchy problem for first order quasilinear hyperbolic systems $$ \left\{ \matrix{ {{\partial u} \over {\partial t}} + {\rm A}\left( u \right){{\partial u} \over {\partial x}} = 0, \hfill \cr t = 0:u = \varphi \left( x \right), \hfill \cr} \right. $$ whereu= (u1, ... ,un)Tis the unknown vector function of (t,x),A(u) = (aij(u))is ann×nmatrix with suitably smoothentricsaij(u) (i,j=1, ... ,n) andφ(x) = (φ1(x), ... ,φn(x))Tis aC1vector function ofxwith boundedC1norm.