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Semilinear elliptic and parabolic equations of arbitrary order

Published online by Cambridge University Press:  24 February 2017

Wolf von Wahl  and
J. B. McLeod
Wolf von Wahl
Affiliation:
Institut für Mathematik der Universität Bochum
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Extract

In this paper we prove the existence of classical solutions for all t ≧ 0 for parabolic equations u′ + A(t)u = –f(u, ∇y, …, ∇2m–2u) of arbitrary order. 2m is the order of the elliptic principal part. f must satisfy some monotonicity and growth conditions. Moreover, similar results are also valid for semilinear elliptic equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 3-4 , 1978 , pp. 193 - 207
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

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