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On product formulas for nonlinear semigroups

Marsden, J. E. (1973) On product formulas for nonlinear semigroups. Journal of Functional Analysis, 13 (1). pp. 51-72. ISSN 0022-1236. doi:10.1016/0022-1236(73)90066-9.

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We study a number of sufficient conditions which guarantee the convergence of semigroup product formulas of the type H_t = lim n∞(F_(t/n)^oG_(t/n))^n and its generalizations. Our hypotheses differ from those of other authors in that we do no assume in advance that the limit operator is a generator. Rather this is a consequence and hence the above formula yields an existence theorem (local in time) for nonlinear semigroups. A number of smoothness properties are studied as well. The results may be applied to and are motivated by the Navier-Stroke equations.

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Additional Information:© 1973 Academic Press. Communicated by Tosio Kato. Received August 2, 1972. Available online 29 June 2004. Some of the ideas in this paper were obtained in col1aboration with David G. Ebin, SUNY at Stony Brook, N.Y. 11790. Partially supported by NSF grant GP 11735.
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NSFGP 11735
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ID Code:19633
Deposited By: Ruth Sustaita
Deposited On:08 Sep 2010 16:19
Last Modified:08 Nov 2021 23:53

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