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Non-autonomous Second Order Differential Inclusions with a Stabilizing Effect
Results in Mathematics ( IF 2.2 ) Pub Date : 2020-12-23 , DOI: 10.1007/s00025-020-01305-1
Tiziana Cardinali , Eleonora De Angelis

In this paper we prove the existence of mild solutions for a problem governed by a semilinear non-autonomous second order differential inclusion where a stabilization of the solution is expected due to the control of the reaction term. In order to obtain our existence theorem, first we study a more general problem with a differential inclusion which involves a perturbation guided by an operator \(N :I \rightarrow C(C(I;X);X)\), where X is a Banach space. Finally we show an illustrative example of application of our results to a problem involving a wave equation.



中文翻译:

具有稳定作用的非自治二阶微分包含

在本文中,我们证明了由半线性非自治二阶微分包含控制的问题的温和解的存在,在该问题中,由于反应项的控制,预计溶液的稳定性。为了获得存在定理,首先我们研究一个微分包含的更一般的问题,它涉及由算符\(N:I \ rightarrow C(C(I; X); X)\)引导的扰动,其中X是一个Banach空间。最后,我们给出了将我们的结果应用于涉及波动方程的问题的说明性示例。

更新日期:2020-12-23
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