Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T10:40:54.557Z Has data issue: false hasContentIssue false

A generalized Hankel transform and its use for solving certain partial differential equations

Published online by Cambridge University Press:  17 February 2009

I. Ali
Affiliation:
Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969 Safat, Kuwait 13060
S. Kalla
Affiliation:
CIMA, Facultad de Ingenería, Universidad del Zuila, Apartado - 10182, Maracaibo, Venezuela
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We introduce a generalized form of the Hankel transform, and study some of its properties. A partial differential equation associated with the problem of transport of a heavy pollutant (dust) from the ground level sources within the framework of the diffusion theory is treated by this integral transform. The pollutant concentration is expressed in terms of a given flux of dust from the ground surface to the atmosphere. Some special cases are derived.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Barenblatt, G. I., “Motion particles in turbulent flow occupying a half space or a flat duct of finite depth”, Prikl. Mat. i Mekh. 17 (1953) 261274.Google Scholar
[2]Barenblatt, G. I., “Motion of suspended particles in turbulent flow”, Prikl. Mat. i Mekh. 19 (1955) 6188.Google Scholar
[3]Berlyand, M. Ye., Sovremennyye problemy atmosfernoy diffuzii i zagryazneniya atmosfery (Problems of atmospheric diffusion and pollution) (Gidrometeorizdat Press, Leningrad, 1975).Google Scholar
[4]Byutner, E. K., Dinamika pripoverkhostnogo sloya vozdukha (Dynamics of the ground-level air layer) (Gidrometeorizdat Press, Leningrad, 1978).Google Scholar
[5]Davies, B., Integral Transforms and Their Applications (Springer-Verlag, New York, 1978).CrossRefGoogle Scholar
[6]Erdelyi, A., Higher Transcendental Functions, 3 volumes (McGraw-Hill, New York, 19531954).Google Scholar
[7]Kalla, S. L. and Urribarri, E., “Hankel transform to the diffusion of dust problem”, in Proc. 5-th. Int. Colloquium Diff. Eq. (Plovdiv, Bulgaria, 1994), 173180.Google Scholar
[8]Lebedev, N. N., Special Functions and their Applications (Prentice-Hall, Englewood Cliffs, N.J., 1965).CrossRefGoogle Scholar
[9]Onikul, R. I. and Khurshudyan, L. G., “The diffusion of dust from its ground-level aerial sources”, Fluid Mechanics-Soviet Research 13 (1984) 6474.Google Scholar
[10]Prudnikov, A. P., Brychkov, Yu. A. and Marichev, O. I., Integrals and Series (Gordon and Breach Science Publishers, Reading, U.K., 1992).Google Scholar
[11]Sneddon, I. N., The use of Integral Transforms (McGraw-Hill, New York, 1972).Google Scholar
[12]Tranter, C. J., Integral Transforms in Mathematical Physics (Chapman and Hall, London, 1971).Google Scholar
[13]Watson, G. N., A Treatise on the theory of Bessel functions (Cambridge Univ. Press, London, 1980).Google Scholar