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Some Remarks on Functional Analysis

Blowey, James F. and Straughan, Brian (2014) 'Some Remarks on Functional Analysis.', in Encyclopedia of Thermal Stresses. Dordrecht: Springer.

Abstract

Functional analysis is a key tool in the study of partial differential equations which helps to answer key questions such as existence, well-posedness, and the class in which a solution should belong. We begin these remarks by introducing normed spaces and Banach spaces and then bounded linear operators in normed spaces. Next, we define Hilbert spaces and consider aspects relating to linear operators on Hilbert spaces. With this structure, we are able to consider well-posed of problems and describe the notions of Hölder and Lyapunov stability and Hadamard well-posedness. Finally, we describe how some thermal stress problems can be formulated using abstract operator notation.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
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Status:Public
Publisher Web site:https://doi.org/10.1007/978-94-007-2739-7_24
Publisher statement:This a post-peer-review, pre-copyedit version of a chapter published in Encyclopedia of Thermal Stresses. The final authenticated version is available online at: https://doi.org/10.1007/978-94-007-2739-7_24
Date accepted:No date available
Date deposited:27 October 2021
Date of first online publication:2014
Date first made open access:27 October 2021

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