Abstract Cauchy problems that involve a product of two Euler-Poisson-Darboux operators

Inhomogeneous Two-Parameter Abstract Cauchy Problem

Adomian Decomposition Method On Nonlinear Singular Cauchy Problem of Euler-Poisson- Darbuox equation

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

The Euler-poisson-darboux Equation in the Exceptional Cases1

where in the EPD equation (1.1) it is understood that Aw = 2Zf=i «*,•*< and k is a parameter, — °° < k < °°. We designate a solution of Li[w]=0 by um(x, t), writing x in place of *i, ■ • • , xm. While particular results for this famous equation go back to Poisson and even to Euler, a systematic investigation of the Cauchy problem covering all values of k and m is of recent date. The results may...

inhomogeneous two-parameter abstract cauchy problem

Abstract Cauchy problems and stochastic integral equations

Cauchy problems and stochastic integral equations Bachelor thesis, June 21, 2011 Thesis supervisor: dr. O. van Gaans Mathematisch Instituut, Universiteit Leiden