Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (4): 460-468.

• Articles • Previous Articles     Next Articles

GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY

 ZHENG Yong-Shu   

  1. Department of Mathematics, Huaqiao University, Quanzhou 362011, China
  • Online:2001-10-06 Published:2001-10-06
  • Supported by:

    Project supported by the NSF of Fujian Province (A97020)

Abstract:

This article considers Cauchy problem ut − (uv)x = 0, vt − ux = 0, (E) u(x, 0) = u0(x) > 0, v(x, 0) = v0(x). (I) A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global C1-solution on t  0 is obtained.

Key words: Nonlinear hyperbolic system, Cauchy problem, global C1-solution

CLC Number: 

  • 35L60
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