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Linear initial value problems with a singular perturbation of hyperbolic type

Published online by Cambridge University Press:  14 November 2011

R. Geel
R. Geel
Affiliation:
Ubbo Emmius Institute, Department of Mathematics, Postbus 2056, 9704 CB Groningen, The Netherlands
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Synopsis

This paper deals with initial value problems in ℝ2 which are governed by a hyperbolic differential equation containing a small positive factor ε in front of the second order part of the differential operator. Pointwise a priori estimates for the solution are established by means of an energy integral method. With the help of these estimates it is shown that the solution admits an asymptotic expansion into powers of ε which is uniformly valid in compact subsets of ℝ2. All results are obtained under the assumption that the characteristics of the first order part of the differential operator satisfy a so-called “timelike” condition. A discussion of the concepts “timelike” and “spacelike” is given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 167 - 187
Copyright
Copyright © Royal Society of Edinburgh 1981

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