Profile of Blow-up Solution to Hyperbolic System with Nonlocal Term

Authors
Duan, Zhi Wen Kim, Kwang Ik
Citation
Duan, Zhi Wen et Kim, Kwang Ik, Profile of Blow-up Solution to Hyperbolic System with Nonlocal Term, Acta mathematica Sinica. English series (Print) , 23(6), 2007, pp. 1083-1094
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
23
Issue
6
Year of publication
2007
Pages
1083 - 1094
Database
ACNP
SICI code
Abstract
This paper is concerned with a nonlocal hyperbolic system as follows: ..utt=.u+(..vdx)pforx.RN,t>0,vtt=.v+(..udx)qforx.RN,t>0,u(x,0) =u0(x),ut(x,0)=u01(x)forx.RN,v(x,0)=v0(x),vt(x,0)=v01(x)forx.RN, where 1 . N . 3, p . 1, q . 1 and pq > 1. Here the initial values are compactly supported and . . .N is a bounded open region. The blow-up curve, blow-up rate and profile of the solution are discussed.