Coefficient recovery in parabolic initial boundary value problems

We consider the inverse problem of identifying spatially dependent coefficients in linear, parabolic, partial differential equations with specified initial and boundary conditions. We primarily explore the recovery of the diffusivity coefficient in the heat equation using a very limited amount of data on a portion of the spatial boundary. In the process, we show that the coefficient dependent observation operator is injective. With this knowledge, we use the Backus-Gilbert approach, modified with an adjoint method, to construct an approximate solution to the problem. We show the results of numerical experiments for the single, spatial variable case and then apply the method to related problems.

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

2006

Authors dc:creator

• Kull, Trent C., author
• DuChateau, Paul, advisor
• Allgower, Eugene L., committee member
• Butters, Greg, committee member
• Mueller, Jennifer, 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/10.25675/3.026452

OAI identifier oai:identifier

oai:mountainscholar.org:10217/243732