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On the generalized heat-equation

Published online by Cambridge University Press:  20 January 2009

C. Nasim  and
B. D. Aggarwala
C. Nasim
Affiliation:
Department of MathematicsUniversity of CalgaryCalgary, AlbertaCanada T2N 1N4
B. D. Aggarwala
Affiliation:
Department of MathematicsUniversity of CalgaryCalgary, AlbertaCanada T2N 1N4
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The general heat equation is defined as

where v is a fixed positive number and α is a fixed number. If v = α = 0, then (1.1) reduces to the ordinary heat equation

where u(x,t) is regarded as the temperature at a point x at time t, in an infinite insulated rod extended along the x-axis in the xt-plane. If we set , then (1.1) becomes

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 3 , October 1984 , pp. 261 - 273
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

1.Haimo, D. T. and Cholewinski, F. M.The Weierstrass Hankel Convolution transform, J. d'Analyse Math. 17 (1966), 1–58.Google Scholar
2.Erdelyi, et al. , Tables of Integral Transforms, Vol. I (McGraw-Hill Book Co., Toronto, 1954).Google Scholar
3.Erdelyi, et al. , Tables of Integral Transforms, Vol. II (McGraw-Hill Book Co., Toronto, 1954).Google Scholar
4.Haimo, D. T. and Cholewinski, F. M.Inversion of the reduced Poisson-Hankel transform, J. d'Analyse Math. 25 (1972), 323–343.CrossRefGoogle Scholar
5.Sneddon, I. N.The Use of Integral Transforms (McGraw-Hill Book Co., Toronto. 1972).Google Scholar