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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nonlinear evolution equations and product integration in Banach spaces.

Author: G. F. Webb
Journal: Trans. Amer. Math. Soc. 148 (1970), 273-282
MSC: Primary 47.65; Secondary 34.00
MathSciNet review: 0265992
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Abstract: The method of product integration is used to obtain solutions to the nonlinear evolution equation $g’ = Ag$ where A is a function from a Banach space S to itself and g is a continuously differentiable function from $[0,\infty )$ to S. The conditions required on A are that A is dissipative on S, the range of $(e - \varepsilon A) = S$ for all $\varepsilon \geqq 0$, and A is continuous on S.

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Keywords: Nonlinear evolution equations, product integration, dissipative mapping, semigroup of nonlinear nonexpansive transformations, infinitesimal generator
Article copyright: © Copyright 1970 American Mathematical Society