Some Notes on the Controllability in a Steady State for the Q-W Equations With Weak Decay
Shuxian Deng, Hongen Li
Available Online February 2017.
- https://doi.org/10.2991/emcm-16.2017.204How to use a DOI?
- Steady; Controllability; Weak; State
- We present a new method of investigating the so-called quasilinear strongly-damped wave equations in this paper, we concerned with the Controllability in a steady state for the Quasilinear Wave Equations with weak decay, and we use a so-called energy perturbation method to establish weak controllability of solutions in terms of energy norm for a class of nonlinear functions. This method allows us to establish the existence and uniqueness of energy solutions. We also established the existence of finite-dimensional global and exponential attractors for the solution semigroup associated with that equation and their additional regularity. We show the controllability in a steady state with the help of differential inequalities by estimating the relationship between energy inequalities and attenuating property of weak solutions. We determine a small positive number and derive differential inequalities by using a perturbation of energy.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - CONF AU - Shuxian Deng AU - Hongen Li PY - 2017/02 DA - 2017/02 TI - Some Notes on the Controllability in a Steady State for the Q-W Equations With Weak Decay BT - 2016 7th International Conference on Education, Management, Computer and Medicine (EMCM 2016) PB - Atlantis Press SN - 2352-538X UR - https://doi.org/10.2991/emcm-16.2017.204 DO - https://doi.org/10.2991/emcm-16.2017.204 ID - Deng2017/02 ER -