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801.
This article deals with the notions of Lyapunov stability and attraction of semiflows on fiber bundles. The focus of the studies is the question on the existence of global attractors in bundles associated to principal bundles. Applications to right invariant systems are presented. 相似文献
802.
We investigate control problems for wave–Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have applications in viscoelasticity theory and linear acoustic theory. 相似文献
803.
804.
Animikh Biswas Ciprian Foias Cecilia F. Mondaini Edriss S. Titi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(2):295-326
Based on a previously introduced downscaling data assimilation algorithm, which employs a nudging term to synchronize the coarse mesh spatial scales, we construct a determining map for recovering the full trajectories from their corresponding coarse mesh spatial trajectories, and investigate its properties. This map is then used to develop a downscaling data assimilation scheme for statistical solutions of the two-dimensional Navier–Stokes equations, where the coarse mesh spatial statistics of the system is obtained from discrete spatial measurements. As a corollary, we deduce that statistical solutions for the Navier–Stokes equations are determined by their coarse mesh spatial distributions. Notably, we present our results in the context of the Navier–Stokes equations; however, the tools are general enough to be implemented for other dissipative evolution equations. 相似文献
805.
Birgit Jacob Felix L. Schwenninger Hans Zwart 《Journal of Differential Equations》2019,266(10):6284-6306
We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial differential equations. Here, we focus on parabolic equations which allow for operator-theoretic methods such as the holomorphic functional calculus. Moreover, we investigate stronger conditions than continuity leading to input-to-state stability with respect to Orlicz spaces. This also implies that the notions of input-to-state stability and integral-input-to-state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite-dimensional. 相似文献
806.
The pronounced cusp in K→3π decays which is generated by the pion mass difference is directly related to the ππS-wave scattering lengths. We apply a nonrelativistic effective field theory framework to evaluate the amplitudes for KL→3π decays in a systematic manner. Electromagnetic effects in the neutral channel KL→3π0 are also discussed. 相似文献
807.