Some applications of generalized exponentials to partial differential equations

Author:
J. Abramowich

Journal:
Proc. Amer. Math. Soc. **89** (1983), 239-245

MSC:
Primary 35C10; Secondary 35G05

DOI:
https://doi.org/10.1090/S0002-9939-1983-0712630-8

MathSciNet review:
712630

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Abstract | References | Similar Articles | Additional Information

Abstract: Using what may be considered as a natural generalization of the exponential function, some of the formalism of the theory of ordinary linear differential equations is extended to a class of linear partial differential equations among which are some important equations of mathematical physics.

In we give the definitions of the generalized exponentials and derive expressions for them. is devoted to the study of some of the properties of the exponential in two independent variables. In we derive the general solutions of some key partial differential equations using the method of recursion. The last section is devoted to extending the formalism of the method of variation of parameters to a class of linear partial differential equations.

**[1]**E. L. Ince,*Ordinary Differential Equations*, Dover Publications, New York, 1944. MR**0010757****[2]**R. Courant and D. Hilbert,*Methods of mathematical physics. Vol. I*, Interscience Publishers, Inc., New York, N.Y., 1953. MR**0065391****[3]**A. N. Tikhonov and A. A. Samarskii,*Equations of mathematical physics*, Translated by A. R. M. Robson and P. Basu; translation edited by D. M. Brink. A Pergamon Press Book, The Macmillan Co., New York, 1963. MR**0165209**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0712630-8

Keywords:
Generalized exponentials,
linear partial differential equations,
variation of parameters,
recursion

Article copyright:
© Copyright 1983
American Mathematical Society