Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (1): 54-70.

• Articles • Previous Articles     Next Articles

BV Solutions for the Quasilinear Hyperbolic Equation with Nonlinear Source and Finite Radon Measure as Initial Conditions

YUAN Hong-Jun, TONG Li-Ning   

  1. Institute of Mathematics, Jilin University, Changchun |130012
  • Received:2007-05-25 Revised:2009-04-12 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    国家自然科学基金(10571072)、教育部高等学校优秀青年教师教学和科研奖励基金([2000]26)、国家重点研究计划973项目基金(2006CB805902)和符号计算与知识工程 教育部重点实验室、吉林大学985项目基金资助.

Abstract:

The aim of this paper is to discuss the Cauchy problem of the quasilinear hyperbolic equation of the form
ut+(um)x=up
with nonnegative finite Radon measures as initial conditions, where m>1,1<p<m are some given real numbers. In particular, the existence and uniqueness of BV solutions for the above problem is obtained.

Key words: Quasilinear hyperbolic equation, BV solutions, Existence and uniqueness

CLC Number: 

  • 22E46
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