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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On nonlinear evolution operators associated with some nonlinear dispersive equations

Authors: Shinnosuke Oharu and Tadayasu Takahashi
Journal: Proc. Amer. Math. Soc. 97 (1986), 139-145
MSC: Primary 35Q20; Secondary 47H20, 58D25
MathSciNet review: 831403
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Abstract: The initial-boundary value problem for a nonlinear dispersive system with time-dependent boundary condition is discussed in the Sobolev space $ {H^1}$ from the point of view of the theory of nonlinear evolution operators. A notion of weak solution to the problem is introduced and the associated family of solution operators is constructed in such a way that it gives rise to a nonlinear evolution operator with time-dependent domain. Various qualitative properties as well as regularity of the weak solutions are investigated through those of the constructed evolution operator.

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Keywords: Nonlinear dispersive equations, long waves of small amplitude, nonlinear evolution operators
Article copyright: © Copyright 1986 American Mathematical Society