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The equation A(t, u(t))′ + B(t, u(t)) = 0

Published online by Cambridge University Press:  24 October 2008

Bruce Calvert
Bruce Calvert
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
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Extract

The initial value problem for the equation

has been studied recently as a model for long waves in nonlinear dispersive systems. Benjamin, Bona and Mahony (2) introduced this equation as an alternative to the KdV equation of Korteweg-de Vries. Hence, it is referred to as the BBM equation. They studied solutions u(x, t) of the BBM equation for t ≥ 0 and x∈(− ∞, ∞), satisfying u(x, 0) = g(x). Bona and Bryant(1) carried through the study of the BBM equation for t ≥ 0 and x ∈ [0, ∞), satisfying u(x, 0) = g(x) and u(0, t) = h(t). The aim of this paper is to study the equation

where At and Bt are mappings defined on subsets of Banach spaces, especially when At is a second order elliptic operator and B is a differential operator of lower order, defined on an unbounded subset Ω of .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 3 , May 1976 , pp. 545 - 561
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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