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Near Viability of a Set-Valued Map Graph with Respect to a Quasi-Autonomous Nonlinear Inclusion
Journal of Dynamical and Control Systems ( IF 0.9 ) Pub Date : 2019-07-25 , DOI: 10.1007/s10883-019-09455-4
Omar Benniche , Mohammed Hachama

This paper addresses near viability of a set-valued map graph \(\mathcal {G}\) with respect to a quasi-autonomous fully nonlinear differential inclusion of the form y(t) ∈ Ay(t) + F(t,y(t)). We introduce a new notion of A-quasi-tangency when A is a nonlinear m-dissipative set-valued operator. We give necessary and sufficient conditions for \(\mathcal {G}\) to be near viable with respect to the previous differential inclusion. We obtain under weak hypotheses a classical relaxation result stating that each solution of the relaxed differential inclusion can be approximated by a solution of the differential inclusion at any given precision.

中文翻译:

集值映射图关于拟自治非线性包含的近似生存力

附近的设定值映射图的存活力本文地址\(\ mathcal {G} \)相对于一个半自治完全非线性微分包含形式的ÿ ')∈Ý)+ ˚Fyt))。当A是一个非线性的m耗散集值算子时,我们引入A-拟相切的新概念。我们为\(\ mathcal {G} \)提供必要和充分的条件相对于先前的差异包含而言几乎可行。我们在弱假设下获得经典松弛结果,该结果表明,在任何给定精度下,松弛微分包含的每个解都可以通过微分包含的解来近似。
更新日期:2019-07-25
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