Some Remarks on Functional Analysis

Blowey, James F.; Straughan, Brian

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
• Public URL: https://durham-repository.worktribe.com/output/1647039