Generalized d’Alembert Formula for the Wave Equation with Discontinuous Coefficients

被引：0
作者：
D. S. Anikonov
D. S. Konovalova
机构：
[1] Novosibirsk State University,Sobolev Institute of Mathematics
[2] Siberian Branch of the Russian Academy of Sciences,undefined
来源：
Differential Equations | 2019年 / 55卷
关键词：
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider a second-order differential equation that is a mathematical model of transverse vibrations of a string or longitudinal vibrations of an elastic rod. The coefficients of the second derivatives are piecewise constant functions. An existence and uniqueness theorem is proved and an explicit formula is given for the generalized solution of the Cauchy problem.
引用
收藏
页码：270 / 273
页数：3
相关论文
共 6 条
  • [1] Petrova G.(1999)Linear transport equations with discontinuous coefficients Comm. Partial Differential Equations 24 1849-1873
  • [2] Popov B.(1998)One-dimensional transport equations with discontinuous coefficients Nonlinear Anal. 32 891-933
  • [3] Bouchut F.(1991)Local error estimates for discontinuous solutions of nonlinear hyperbolic equations SIAM J. Numer. Anal. 28 891-906
  • [4] Jame F.(1947)Generalization of d’Alembert and Poisson formulas Uspekhi Mat. Nauk 2 175-182
  • [5] Tadmor E.(undefined)undefined undefined undefined undefined-undefined
  • [6] Salekhov G.S.(undefined)undefined undefined undefined undefined-undefined
1