Approximation and control of a thermoviscoelastic system

In this paper consider the problem of controlling a thermoviscoelastic system. We present a semigroup setting for this system, and prove the well-posedness by applying a general theorem which is given in this paper. We also study the stability of the system. We give a finite element/averaging scheme to approximate the linear quadratic regulator problem governed by the system. We prove that yields faster convergence. We give a proof of convergence of the simulation problem for singular kernels and of the control problem for L2 kernels. We carry on the numerical computation to investigate the effect of heat transfer on damping and the closed-loop system.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Polytechnic Institute and State University

Year dc:date.issued

1989

Author dc:creator

• Liu, Zhuangyi

Chair dc:contributor.committeechair

• Burns, John A.

Committee members dc:contributor.committeemember

• Herdman, Terry L.
• Cebuhar, W.A.
• Cliff, Eugene M.
• Hannsgen, Kenneth B.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/10919/54233

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/54233