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Sharp ultimate velocity bounds for the general solution of some linear second order evolution equation with damping and bounded forcing. (English) Zbl 07423283

In the paper under review, the authors prove the equivalence of different notions of optimal bound of solutions to a class of abstract evolution equations (Theorem 2.2). Furthermore, they investigate the optimal velocity bound for both scalar equations \[u^{\prime\prime}(t)+cu^\prime(t)+bu(t)=f(t)\] and vector equations \[u^{\prime\prime}(t)+cu^\prime(t)+Au(t)=f(t).\] The paper is well-written and the subject is of a significant interest.

MSC:

34G10 Linear differential equations in abstract spaces
37C60 Nonautonomous smooth dynamical systems
34D05 Asymptotic properties of solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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