On nonlinear evolution operators associated with some nonlinear dispersive equations

Oharu, Shinnosuke; Takahashi, Tadayasu

doi:10.1090/S0002-9939-1986-0831403-1

On nonlinear evolution operators associated with some nonlinear dispersive equations
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by Shinnosuke Oharu and Tadayasu Takahashi PDF

Proc. Amer. Math. Soc. 97 (1986), 139-145 Request permission

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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