论文标题
尖锐的最终速度边界，用于与阻尼和界强迫的一些线性二阶进化方程的一般解决方案
Sharp ultimate velocity bounds for the general solution of some linear second order evolution equation with damping and bounded forcing
论文作者
论文摘要
我们考虑使用阻尼和外力的一类线性二阶微分方程。我们研究了强迫术语与溶液速度的相应最终结合之间的统一结合之间的联系，并研究了该结合对阻尼和“弹性力”的依赖性。 我们证明了三个结果。首先，在相当普遍的环境中，我们表明，界限的不同概念实际上是等效的。然后，我们在标量情况下计算最佳常数。最后，我们将标量案例的结果扩展到希尔伯特空间中抽象的耗散波型方程。在这种情况下，我们获得了与标量案例完全不同的敏锐估计，在有限和无限的尺寸框架中。 抽象理论特别适用于耗散波，板和梁方程。
We consider a class of linear second order differential equations with damping and external force. We investigate the link between a uniform bound on the forcing term and the corresponding ultimate bound on the velocity of solutions, and we study the dependence of that bound on the damping and on the "elastic force". We prove three results. First of all, in a rather general setting we show that different notions of bound are actually equivalent. Then we compute the optimal constants in the scalar case. Finally, we extend the results of the scalar case to abstract dissipative wave-type equations in Hilbert spaces. In that setting we obtain rather sharp estimates that are quite different from the scalar case, in both finite and infinite dimensional frameworks. The abstract theory applies, in particular, to dissipative wave, plate and beam equations.
