Wheeler, Lewis T.2022-06-222022-06-22197113683551https://hdl.handle.net/10657/9748Recently a new theory of heat conduction has appeared in the literature. The raison d'etre of this theory is that in the classical theory heat propagates in a body with infinite speed. The present paper deals with the linearized form of the theory, which gives rise to an integro-partial differential equation. Two problems for this equation, called history-value problems, are posed. It is shown that, under certain conditions, solutions to these history-value problems on a bounded region of space are unique. Next, it is shown that if the data of the problem have bounded support, then for any time the solution has bounded support. This proves the hypothesis of finite wave speeds. This result is then used to prove that solutions to the history-value problems on an unbounded region of space are unique.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital