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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Necessary and sufficient conditions for viability for semilinear differential inclusions


Authors: Ovidiu Cârja, Mihai Necula and Ioan I. Vrabie
Journal: Trans. Amer. Math. Soc. 361 (2009), 343-390
MSC (2000): Primary 34G20, 47J35; Secondary 35K57, 35K65
Published electronically: August 21, 2008
MathSciNet review: 2439410
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Abstract: Given a set $ K$ in a Banach space $ X$, we define: the tangent set, and the quasi-tangent set to $ K$ at $ \xi\in K$, concepts more general than the one of tangent vector introduced by Bouligand (1930) and Severi (1931). Both notions prove very suitable in the study of viability problems referring to differential inclusions. Namely, we establish several new necessary, and even necessary and sufficient conditions for viability referring to both differential inclusions and semilinear evolution inclusions, conditions expressed in terms of the tangency concepts introduced.


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Additional Information

Ovidiu Cârja
Affiliation: Faculty of Mathematics, “Al. I. Cuza” University, Iaşi 700506, Romania – and – “Octav Mayer” Mathematics Institute, Romanian Academy, Iaşi 700506, Romania
Email: ocarja@uaic.ro

Mihai Necula
Affiliation: Faculty of Mathematics, “Al. I. Cuza” University Iaşi 700506, Romania
Email: necula@uaic.ro

Ioan I. Vrabie
Affiliation: Faculty of Mathematics, “Al. I. Cuza” University, Iaşi 700506, Romania – and – “Octav Mayer” Mathematics Institute, Romanian Academy, Iaşi 700506, Romania
Email: ivrabie@uaic.ro

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04668-0
PII: S 0002-9947(08)04668-0
Keywords: Viability, tangency condition, reaction-diffusion systems, compact semigroup.
Received by editor(s): February 15, 2007
Published electronically: August 21, 2008
Additional Notes: The first and third authors were supported by the Project CEx05-DE11-36/05.10.2005. The second author was supported by CNCSIS Grant A 1159/2006.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.