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Uniqueness of solutions to certain hyperbolic boundary value problems in a semi-infinite strip

Part of: General higher-order equations and systems

Published online by Cambridge University Press:  26 February 2010

C. M. Khalique
C. M. Khalique
Affiliation:
Department of Mathematical Sciences, University of North-West, Private Bag X2046, Mmabatho 2735, South Africa.
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Abstract

It is well known that boundary value problems for hyperbolic equations are in general “not well posed” problems. This paper is concerned with the uniqueness of solutions to boundary value problems for the hyperbolic equation uxx − Qu = utt. Here Q is a function of the variable x alone, and satisfies the following conditions:

(a) Q:[0, ∞) → ℝ;

(b) Q is Lebesgue integrable on any compact subinterval of [0, ∞);

(c) Q(x)→ ∞ as x → ∞.

MSC classification

Secondary: 35G15: Boundary value problems for linear higher-order equations
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 155 - 163
Copyright
Copyright © University College London 1999

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