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Semilinear evolution equations and fractional powers of a closed pair of operators

Published online by Cambridge University Press:  14 November 2011

Marié Grobbelaar-Van Dalsen
Marié Grobbelaar-Van Dalsen
Affiliation:
University of South Africa, P.O. Box 392, 0001 Pretoria, South Africa
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Synopsis

The nonlinear evolution problem [Bu(t)]′ = A(t, Bu)u + f(t, Bu) with B a constant linear operator and A = A(t, Bu) a time-dependent nonlinear operator from one Banach space to another, is studied. Existence and uniqueness results are obtained by making use of the theory of B-evolutions and the fractional powers of A and B. Two examples are presented in which the theory is applied to nonlinear equations with dynamic boundary conditions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 101 - 115
Copyright
Copyright © Royal Society of Edinburgh 1987

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