In mathematics, the Euler–Poisson–Darboux(EPD)[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.
[3][4][5][6] The EPD equation equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, therefore it has an interest as a paradigm to relativity theory.
[7] Compact support self-similar solution of the EPD equation for thermal conduction was derived starting from the modified Fourier-Cattaneo law.
[8] It is also possible to solve the non-linear EPD equations with the method of generalized separation of variables.