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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Trotter's product formula for semigroups generated by quasilinear elliptic operators


Author: Michiaki Watanabe
Journal: Proc. Amer. Math. Soc. 92 (1984), 509-514
MSC: Primary 35K55; Secondary 47H20
MathSciNet review: 760935
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Abstract: Trotter's product formula is given for nonlinear semigroups in $ {L^1}({R^N})$ generated by quasilinear operators of the form $ \Delta \phi $, where $ \phi $ is a suitable function: formally $ \exp (t\Delta \phi )u = {\lim _{h \downarrow 0}}{\left\{ {\exp (h\Delta {\phi _1}) \cdots \exp (h\Delta {\phi _k})} \right\}^{[t/h]}}u$, where $ \phi = {\phi _1} + \cdots + {\phi _k}$. The proof is carried out by a new method for construction of a semigroup with generator $ \Delta \phi $ in $ {L^1}({R^N})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760935-8
PII: S 0002-9939(1984)0760935-8
Keywords: Nonlinear semigroup, Trotter's product formula, quasilinear operator
Article copyright: © Copyright 1984 American Mathematical Society