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V.—On an Elementary Solution of a Partial Differential Equation of Parabolic Type. Part II: The Nature of the Singularity.

Published online by Cambridge University Press:  14 February 2012

E. T. Copson
Affiliation:
University College, Dundee, in the University of St Andrews

Summary

It is shown that the elementary solution Γ(x, ξ; t – τ) of the equation

behaves, as t → τ + O, in very much the same manner as the elementary solution of the equation of heat.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1941

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References

References to Literature

Copson, E. T., 1940. “On an Elementary Solution of a Partial Differential Equation of Parabolic Type. Part I,” Proc. Roy. Soc. Edin., vol. lxi, A, PP. 3753.Google Scholar
Hadamard, J., 1911. “Sur la solution fondamentale des équations aux dérivées partielles du type parabolique,” C.R. Acad. Sci. Paris, vol. clii, pp. 11481149.Google Scholar
Hobson, E. W., 1908. “On a General Convergence Theorem, and the Theory of the Representation of a Function by a Series of Normal Functions,” Proc. London Math. Soc. (2), vol. vi, pp. 349395.CrossRefGoogle Scholar
Hobson, E. W., 1926. The Theory of Functions of a Real Variable, II (2nd ed.), Cambridge.Google Scholar
Husimi, K., 1940. “Some Formal Properties of the Density Matrix,” Proc. Phys. Math. Soc. Japan (3), vol. xxii, pp. 264314.Google Scholar
Ince, E. L., 1927. Ordinary Differential Equations, London.Google Scholar
Whittaker, E. T., and Watson, G. N., 1920. Modern Analysis (3rd ed.), Cambridge.Google Scholar