Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35Q20, 47H20, 58D25

Retrieve articles in all journals with MSC: 35Q20, 47H20, 58D25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0831403-1
PII: S 0002-9939(1986)0831403-1
Keywords: Nonlinear dispersive equations, long waves of small amplitude, nonlinear evolution operators
Article copyright: © Copyright 1986 American Mathematical Society