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Propagation relations for solutions of some higher order cauchy problems

Published online by Cambridge University Press:  17 February 2009

L. R. Bragg
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Abstract

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The Huygens' property is exploited to study propagation relations for solutions of certain types of linear higher order Cauchy problems. Motivated by the solution properties of the abstract wave problem, addition formulas are developed for the solution operators of these problems. The application of these alternative forms of the solution operators to data leads to connecting operator relations between distinct solutions of the problems at different times. We examine this solution behaviour for both analytic and abstract Cauchy problems. A basic algorithm for constructing addition formulas for solutions of ordinary differential equations is included.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 38 , Issue 2 , October 1996, pp. 229 - 239
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Bragg, L. R., “Complex transformations of solutions of generalized initial value heat problems”, Rocky Mtn. Jour. of Math 20 (1990) 677–705.Google Scholar
[2]Bragg, L. R. and Dettman, J. W., “An operator calculus for related partial differential equations”, J. Math Anal Appl 22 (1968) 459–167.CrossRefGoogle Scholar
[3]Carroll, R. W., Transmutations and operator differential equations (North-Holland, Amsterdam, 1979).Google Scholar
[4]Carroll, R. W., Transmutation theory and applications (North-Holland, Amsterdam, 1985).Google Scholar
[5]Goldstein, J., Semigroups of linear operators and applications (Clarendon Press, Oxford, 1985).Google Scholar
[6]Rosenbloom, P. C. and Widder, D. V., “Expansions in terms of heat polynomials and associated functions”, Trans. Amer. Math. Soc. 92 (1959) 220–266.CrossRefGoogle Scholar