Some Remarks on Functional Analysis

Blowey, James F.; Straughan, Brian

doi:10.1007/978-94-007-2739-7_24

Some Remarks on Functional Analysis

Blowey, James F.; Straughan, Brian

Authors

Professor James Blowey j.f.blowey@durham.ac.uk
Deputy Exec Dean & Dir Of Natural Scs

Brian Straughan

Contributors

Richard B. Hetnarski
Editor

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.

Citation

Blowey, J. F., & Straughan, B. (2014). Some Remarks on Functional Analysis. In R. B. Hetnarski (Ed.), Encyclopedia of Thermal Stresses. Springer Verlag. https://doi.org/10.1007/978-94-007-2739-7_24

Publication Date	2014
Deposit Date	Oct 26, 2021
Publicly Available Date	Oct 27, 2021
Publisher	Springer Verlag
Book Title	Encyclopedia of Thermal Stresses
ISBN	9789400727380
DOI	https://doi.org/10.1007/978-94-007-2739-7_24

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Copyright 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