Invariance for quasi-dissipative systems in Banach spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:457

Article

Cannarsa, P.¹  Da Prato, G.²  Frankowska, H.³ 

[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci 1, I-00133 Rome, Italy

[2] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56125 Pisa, Italy

[3] UPMC Univ Paris 06, Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche, CNRS,UMR 7586, Case 247,4 Pl Jussieu, F-75252 Paris, France

关键词: Evolution equations;    Invariance;    Dissipative operators;    Distance function;   

DOI  :  10.1016/j.jmaa.2016.11.087

来源: Elsevier

【 摘 要 】

In a separable Banach space E, we study the invariance of a closed set K under the action of the evolution equation associated with a maximal dissipative linear operator A perturbed by a quasi-dissipative continuous term B. Using the distance to the closed set, we give a general necessary and sufficient condition for the invariance of K. Then, we apply our result to several examples of partial differential equations in Banach and Hilbert spaces. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free