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2019 | OriginalPaper | Chapter

4. Existence/Uniqueness Results for Parabolic PDEs

Authors : Iasson Karafyllis, Miroslav Krstic

Published in: Input-to-State Stability for PDEs

Publisher: Springer International Publishing

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Abstract

Existence and uniqueness results for 1-D, parabolic PDEs which are in feedback interconnection with a system of ODEs are provided in the chapter. The obtained results allow the presence of nonlinear and non-local terms and guarantee the existence of classical solutions. The existence/uniqueness results are utilized in two applications with non-local terms: a chemical reactor in which an exothermic chemical reaction is taking place and a water tank. Finally, the case where boundary inputs are present is also studied.

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previous chapter ISS in Spatial L p Norms for Hyperbolic PDEs
next chapter ISS in Spatial L2 and H1 Norms
Literature
1.
Boyce WE, Diprima RC (1997) Elementary differential equations and boundary value problems, 6th edn. Wiley, New York
2.
Naylor AW, Sell GR (1982) Linear operator theory in engineering and science. Springer, BerlinCrossRef
3.
Orlov Y (2017) On general properties of eigenvalues and eigenfunctions of a Sturm-Liouville operator: comments on “ISS with respect to boundary disturbances for 1-D parabolic PDEs”. IEEE Trans Autom Control 62:5970–5973MathSciNetCrossRef
4.
Pazy A (1983) Semigroups of linear operators and applications to partial differential equations. Springer, New YorkCrossRef
Metadata
Title
Existence/Uniqueness Results for Parabolic PDEs
Authors
Iasson Karafyllis
Miroslav Krstic
Copyright Year
2019
Book
Input-to-State Stability for PDEs

Print ISBN: 978-3-319-91010-9

Electronic ISBN: 978-3-319-91011-6

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-91011-6_4