Adjoint approach to parameter identification with application to the Richards equation

The inverse problem for the unknown coefficient ingredient of a class of quasilinear parabolic partial differential equations is considered. An approach based on utilizing adjoint versions of the direct problems to derive integral equations explicitly relating changes in inputs (coefficients) to changes in outputs (measured data) is presented. Using the integral equations it is possible to demonstrate properties of these maps. In the first problem, we show that the coefficient to data mappings are continuous, strictly monotone and injective. In the second, the mapping is shown to be explicitly invertible. The equations are further exploited to construct an approximate solution to the inverse problem. In the first problem, these equations are also used to analyze the error in the approximation. These equations are then used to construct a numerical recovery algorithm, which we call the integral identity method. Finally, numerical experiments are presented which explore the recovery process.

Name thesis:degree_name

Doctor of Philosophy (Ph.D.)

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

Colorado State University. Libraries

Year dc:date.issued

2004

Authors dc:creator

• Thelwell, Roger, author
• DuChateau, Paul, advisor
• Butters, Greg, committee member
• Tavener, Simon J., committee member
• Zachmann, David W., committee member

• mathematics

Statement dc:rights

• Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.25675/3.026044

OAI identifier oai:identifier

oai:mountainscholar.org:10217/243190