A new integral transform and associated distributions. (English) Zbl 1191.35017

Eltayeb, Hassan; Kılıçman, Adem; Fisher, Brian

Integral Transforms Spec. Funct. 21, No. 5-6, 367-379 (2010).

Summary: We generalize the concepts of a new integral transform, namely the Sumudu transform, to distributions and study some of their properties. Further, we also apply this transform to solve one-dimensional wave equation having a singularity at the initial conditions.

MSC:

35A22	Transform methods (e.g., integral transforms) applied to PDEs
44A35	Convolution as an integral transform

Keywords:

one-dimensional wave equation; singularity at the initial conditions; Sumudu transform; PDE(s) with variable coefficients; double convolution; distributions

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