zbMATH — the first resource for mathematics

A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform. (English) Zbl 1184.35009
Summary: We consider general linear second-order partial differential equations and we solve three fundamental equations by replacing the non-homogeneous terms with double convolution functions and data by a single convolution.

35A22 Transform methods (e.g., integral transforms) applied to PDEs
Full Text: DOI
[1] lamb, G.L., Introductory applications of partial differential equations with emphasis on wave propagation and diffusion, (1995), John Wiley and Sons New York · Zbl 0864.35004
[2] Myint-U. Tyn, Partial Differential Equations of Mathematical Physics, New York, 1980 · Zbl 0428.35001
[3] Christian Constanda, Solution Techniques for Elementary Partial Differential Equations, New York, 2002 · Zbl 1042.35001
[4] Duffy, Dean G., Transform methods for solving partial differential equations, (2004), CRC · Zbl 1073.35001
[5] Sneddon, N.; Ulam, S.; Stark, M., Operational calculus in two variables and its applications, (1962), Pergamon Press Ltd
[6] Ali Babakhani, R.S. Dahiya, Systems of multi-dimenstional Laplace transform and heat equation, in: 16th conference on Applied Mathematics, Univ. of Central Oklahoma, Electronic Journal of Differential Equations Conf. 07, 2001, pp. 25-36 · Zbl 0977.44002
[7] Brychkov, Yu.A.; Glaeske, H.J.; Prudnikov, A.P.; Tuan, Vu Kim, Multidimensional integral transformations, (1992), Gordon and Breach Science Publishers · Zbl 0752.44004
[8] Adem Kılıçman, Hassan Eltayeb, A note on the non-constant coefficient linear second order partial differential equation, the paper presented in the Fourth Inter. Conf. of Appl Math. and Computing, Aug 12-18, Plovdiv, Bulgaria, 2007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.