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oai:mountainscholar.org:10217/2437322026-03-17T11:09:54Zcom_10217_100532com_10217_100000com_10217_100468com_10217_100303col_10217_100538col_10217_100469

Kull, Trent C., author DuChateau, Paul, advisor Allgower, Eugene L., committee member Butters, Greg, committee member Mueller, Jennifer, committee member 2026-03-16T18:25:15Z 2006 https://hdl.handle.net/10217/243732 https://doi.org/10.25675/3.026452 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. doctoral dissertations English eng Colorado State University. Libraries 2000-2019 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. Per the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users. mathematics Coefficient recovery in parabolic initial boundary value problems Text Doctor of Philosophy (Ph.D.) Doctoral Mathematics Colorado State University This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). open.access