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 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0831403-1

Keywords:
Nonlinear dispersive equations,
long waves of small amplitude,
nonlinear evolution operators

Article copyright:
© Copyright 1986
American Mathematical Society