# Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients

Open Mathematics (2011)

- Volume: 9, Issue: 2, page 269-280
- ISSN: 2391-5455

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topHengyan Li, and Shuguan Ji. "Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients." Open Mathematics 9.2 (2011): 269-280. <http://eudml.org/doc/269592>.

@article{HengyanLi2011,

abstract = {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.},

author = {Hengyan Li, Shuguan Ji},

journal = {Open Mathematics},

keywords = {Optimal control; Periodic wave equation; Weak solution; Arzelà-Ascoli lemma; Sobolev compact imbedding theorem; optimal control; periodic wave equation; weak solution},

language = {eng},

number = {2},

pages = {269-280},

title = {Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients},

url = {http://eudml.org/doc/269592},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Hengyan Li

AU - Shuguan Ji

TI - Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients

JO - Open Mathematics

PY - 2011

VL - 9

IS - 2

SP - 269

EP - 280

AB - 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.

LA - eng

KW - Optimal control; Periodic wave equation; Weak solution; Arzelà-Ascoli lemma; Sobolev compact imbedding theorem; optimal control; periodic wave equation; weak solution

UR - http://eudml.org/doc/269592

ER -

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