Electron. J. Diff. Equ., Vol. 2016 (2016), No. 165, pp. 1-7.

Singularities of solutions to partial differential equations in a complex domain

Naouel Bentiba

Abstract:
We give an explicit representation of the solution of the following singular Cauchy problem with analytic data,
$$ u_{tt}-xu_{xx}+Cu_{x}-B(t^2-4x)^{-1}u=0. $$
We also study the singularities of this solution.

Submitted May 4, 2016. Published June 28, 2016.
Math Subject Classifications: 35A20, 35C10, 33C05, 33B15.
Key Words: Cauchy problem; singular solutions; hypergeometric equation.

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Naouel Bentiba
Department of Mathematics
Faculty of Sciences
University Badji Mokhtar Annaba
23000 Annaba, Algeria
email: nabn_math@hotmail.com

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