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On reflection principles for parabolic equations in one space variable*

Published online by Cambridge University Press:  20 January 2009

David Colton
David Colton
Affiliation:
University of Strathclyde Glasgow
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In this note we shall consider the problem of uniquely continuing solutions of the parabolic equation

across an analytic arc σ: x=s1(t) satisfies the boundary data

We assume that u(x,t) is a classical solution of (1) in the domain D ={(x,t): s1(t)< x < s 2(t), 0 < t < t0}, continuously differentiate in D ∪ σ and define the “reflection” of D across σ by

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 2 , September 1978 , pp. 143 - 147
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

REFERENCES

(1) Colton, D., Solution of Boundary Value Problems by the Method of Integral Operators (Pitman Press, London, 1976).Google Scholar
(2) Colton, D., Integral operators and reflection principles for parabolic equations in one space variable, J. Diff. Eqns. 15 (1974), 551–559.CrossRefGoogle Scholar
(3) Colton, D., Generalized reflection principles for parabolic equations in one space variable, Duke Math. J. 41 (1974), 547–553.CrossRefGoogle Scholar
(4) Garabedian, P., Partial Differential Equations (John Wiley, New York, 1964).Google Scholar
(5) Widder, D., The Heat Equation (Academic Press, New York, 1975).Google Scholar