数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (2): 121-129.

• 论文 •    下一篇

CAUCHY PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER ORDER WITH DISCONTINUOUS INITIAL DATA CAUCHY PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER ORDER WITH DISCONTINUOUS INITIAL DATA

陈恕行   

  1. Inst. of Math., Fudan Univ., Shanghai 200433, China
  • 收稿日期:1991-11-22 出版日期:1994-06-25 发布日期:1994-06-25

CAUCHY PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER ORDER WITH DISCONTINUOUS INITIAL DATA CAUCHY PROBLEM FOR SEMILINEAR HYPERBOLIC EQUATION OF HIGHER ORDER WITH DISCONTINUOUS INITIAL DATA

Chen Shuxing   

  1. Inst. of Math., Fudan Univ., Shanghai 200433, China
  • Received:1991-11-22 Online:1994-06-25 Published:1994-06-25

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摘要： In this paper the following Cauchy problem is under considerabon,
Lu=F(t,x1,…,u,xm,…,∂m-1u) ∂m-1ut=0=q (j=1,…,m) where L is a strictly hyperbolic operator of m-th Order with respect to direction t, F is a C∞ function of its arguments, the initial data have discontinuity along a smooth submanifold with codimentional 1 on initial plane and some conormal regularity with respect to manifold.

Abstract: In this paper the following Cauchy problem is under considerabon,
Lu=F(t,x1,…,u,xm,…,∂m-1u) ∂m-1ut=0=q (j=1,…,m) where L is a strictly hyperbolic operator of m-th Order with respect to direction t, F is a C∞ function of its arguments, the initial data have discontinuity along a smooth submanifold with codimentional 1 on initial plane and some conormal regularity with respect to manifold.

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