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A certain boundary value problem and its applications

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Summary

In the present paper a linear second order partial differential system arising in mathematical physics is solved with the help of Laplace transforms, involving more general boundary conditions, in terms of Mathieu functions. Four physical problems are presented and it is indicated that their solutions can be deduced as a particular case.

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References

  1. McLachlan, N. W., Theory and application of Mathieu functions, Oxford, 1951.

  2. Carslaw, H. S. and J. C. Jaeger, Conduction of heat in Solids, Oxford, 1957.

  3. Strutt, M. J. O., Ann. Phys. Lpz. 84 (1927) 485.

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  4. Carslaw, H. S. and J. C. Jaeger, Ibid, p. 277.

  5. Izumi, Ryotaro, Natural heat convection inside the vertical tube, Proc. of 6th Japan National Congress for Applied Mechanics, 1956, p. 394.

  6. Tables relating to Mathieu functions, Columbia University Press, New York, 1951.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology, Kharagpur, India

    O. P. Bhutani

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  1. O. P. Bhutani
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Bhutani, O.P. A certain boundary value problem and its applications. Appl. sci. Res. 8, 413–424 (1959). https://doi.org/10.1007/BF00411767

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  • DOI: https://doi.org/10.1007/BF00411767

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