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)

 

Time dependent nonlinear Cauchy problems in Banach spaces


Author: W. E. Fitzgibbon
Journal: Proc. Amer. Math. Soc. 36 (1972), 525-530
MSC: Primary 34G05
MathSciNet review: 0308539
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The method of product integration is used to obtain solutions to the nonlinear evolution equation $ u'(t) + A(t)u(t) = 0$ where $ \{ A(t):t \in [0,T]\} $ is a family of nonlinear accretive operators mapping a Banach space X to itself. The main requirements are that $ R(I + \lambda A(t)) \supseteq {\text{cl}}(D(A(t))),D(A(t))$ is time independent, the resolvent $ {(I + \lambda A(t))^{ - 1}}x$ satisfies a local Lipschitz condition, and that each A(t) satisfies Condition M.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34G05

Retrieve articles in all journals with MSC: 34G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0308539-7
PII: S 0002-9939(1972)0308539-7
Keywords: Nonlinear evolution equation, product integration, accretive operator
Article copyright: © Copyright 1972 American Mathematical Society