Some Notes on the Controllability in a Steady State for the Q-W Equations With Weak Decay

DOI

10.2991/emcm-16.2017.204How to use a DOI?

Keywords

Steady; Controllability; Weak; State

Abstract

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.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  - Proceedings of the 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  - 10.2991/emcm-16.2017.204
ID  - Deng2017/02
ER  -