Parameter identification in linear and nonlinear parabolic partial differential equations

The research presented in this dissertation is carried out in two parts; the first, which is the main work of this dissertation, involves development of continuous differentiability of the solution with respect to the unknown parameters. For linear parabolic partial differential equations, only mild conditions are assumed on the admissible parameter space. The nonlinear partial differential equation we consider is a generalized Burgers’ equation, for which we establish the well-posedness and the smoothness properties of the solution with respect to the parameters. In the second part, we consider parameter identification problems for these two parameter dependent systems. The identification scheme which we use here is the quasilinearization method. Based on the results in the first part of this work, we obtain existence and local convergence of the algorithm. We also present some numerical examples which demonstrate the performance of the quasilinearization scheme.

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 Tech

Year dc:date.issued

1995

Author dc:creator

• Zhang, Lan

Chair dc:contributor.committeechair

• Burns, John A.

Committee members dc:contributor.committeemember

• Gunzburger, Max D.
• Herdman, Terry L.
• McCoy, Robert A.
• Peterson, Janet S.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

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

Language dc:language.iso

en

Dc Identifier Other

etd-05112006-154811

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/37762