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Singular first order perturbations of the heat equation

Published online by Cambridge University Press:  14 November 2011

Joel Avrin
Joel Avrin
Affiliation:
Department of Mathematics, Tulane University, New Orleans, LA 70119, U.S.A.
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Synopsis

We exhibit dimension-independent conditions under which the formal operator A = −Δ + a.∇ + V can be defined on such that its closure Ā in L2(Rs, dx) is quasi-m-accretive. Here, a is real so that Ā is nonselfadjoint. the method of proof is a generalized version of the argument employed in the portion of the author's thesis where term a.∇ was originally considered. Specifically, we construct exp (−tĀ) as a limit of approximating semigroups. Since the thesis appeared, Kato has also dealt with the term a. ∇ his conditions on a and V are similar to, but more general than, the conditions that appear here; in addition, he considers magnetic vector potentials. Of interest here is the semigroup method itself, the conciseness of the arguments thereby produced, and a relaxed condition on div a.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 317 - 321
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

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