On Some Convergence Theorem of Double Laplace Transform

Ranjit R. Dhunde, G. L. Waghmare


Starting with convergence and absolute convergence of double Laplace integral uniform convergence of double Laplace transform is presented. Finally, a Volterra Integro-Partial Differential Equation is solved by using double Laplace transform.


Double Laplace transform; Inverse Laplace transform; Integro-Partial differential equation; Partial derivatives

Full Text:



A. Aghili and H. Zeinali, Two-Dimensional Laplace Transforms for Non-homogeneous Forth Order Partial Differential Equations, Journal of

Mathematical Research & Applications, 1(2) (December 2013), 48-54.

A. Estrin and T. J. Higgins, The Solution of Boundary Value Problems by Multiple

Laplace Transformation, Journal of the Franklin Institute, 252 (2) (1951), 153-167.

D. V. Widder, Advanced Calculus, Second Edition, Prentice Hall of India

Private Limited New Delhi, 2005.

G. A. Coon and D. L. Bernstein, Some Properties of the Double Laplace

Transformation, American Mathematical Society, 74 (1953), 135-176.

H. Eltayeb, A. Kilicman and S. Mesloub, Exact Evaluation of Infinite Series Using

Double Laplace Transform Technique, Abstract & Applied Analysis,

, http://dx.doi.org/10.1155/2014/327429, 2014.

Ian N. Sneddon, The Use of Integral Transforms, Tata McGraw Hill, Edition 1974.

J. Debnath and R. S. Dahiya ,Theorems On Multidimensional Laplace Transform For Solution Of Boundary Value Problems, Computers Math. Appli., 18(12) (1989), 1033-1056.

M. M. Moghadam and H. Saeedi, Application of Differential transforms for Solving the Volterra Integro-Partial Differential Equations, Iranian Journal of Science & Technology, Transaction A, 34 (A1) (2010).

R. G. Buschman, Heat transfer between a fluid & a plate: Multidimensional

Laplace Transformation methods, Interat. J. Math. & Math. Sci., 6 (3) (1983), 589-596.

W. F. Trench, Functions defined by Improper Integrals, wtrench@trinity.edu.

DOI: http://dx.doi.org/10.26713%2Fjims.v6i1.242

eISSN 0975-5748; pISSN 0974-875X