Euler–Poisson–Darboux equation

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In mathematics, the Euler–Poisson–Darboux[1][2] equation is the partial differential equation

This equation is named for Siméon Poisson, Leonhard Euler, and Gaston Darboux. It plays an important role in solving the classical wave equation.

This equation is related to

by , , where [2] and some sources quote this equation when referring to the Euler–Poisson–Darboux equation.[3][4][5][6]


  1. ^ Zwillinger, D. (1997). Handbook of Differential Equations 3rd edition. Academic Press, Boston, MA.
  2. ^ a b 1901-1980., Copson, E. T. (Edward Thomas) (1975). Partial differential equations. Cambridge: Cambridge University Press. ISBN 978-0521098939. OCLC 1499723.CS1 maint: numeric names: authors list (link)
  3. ^ Copson, E. T. (1956-06-12). "On a regular Cauchy problem for the Euler—Poisson—Darboux equation". Proc. R. Soc. Lond. A. 235 (1203): 560–572. Bibcode:1956RSPSA.235..560C. doi:10.1098/rspa.1956.0106. hdl:2027/mdp.39015095254382. ISSN 0080-4630.
  4. ^ Shishkina, Elina L.; Sitnik, Sergei M. (2017-07-15). "The general form of the Euler--Poisson--Darboux equation and application of transmutation method". arXiv:1707.04733 [math.CA].
  5. ^ Miles, E.P; Young, E.C (1966). "On a Cauchy problem for a generalized Euler-Poisson-Darboux equation with polyharmonic data". Journal of Differential Equations. 2 (4): 482–487. Bibcode:1966JDE.....2..482M. doi:10.1016/0022-0396(66)90056-8.
  6. ^ Fusaro, B. A. (1966). "A Solution of a Singular, Mixed Problem for the Equation of Euler-Poisson- Darboux (EPD)". The American Mathematical Monthly. 73 (6): 610–613. doi:10.2307/2314793. JSTOR 2314793.

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