This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore, the existence of the optimal control is proved by means of the Arzelà-Ascoli lemma and Sobolev compact imbedding theorem.
@article{bwmeta1.element.doi-10_2478_s11533-010-0098-0,
author = {Hengyan Li and Shuguan Ji},
title = {Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {269-280},
zbl = {1215.49007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0098-0}
}
Hengyan Li; Shuguan Ji. Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients. Open Mathematics, Tome 9 (2011) pp. 269-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0098-0/
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