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Publisher DOI: 10.1007/978-3-030-89397-2_17
Title: Evolutionary inclusions
Language: English
Authors: Seifert, Christian  
Trostorff, Sascha 
Waurick, Marcus 
Issue Date: 28-Sep-2021
Publisher: Springer
Source: Operator Theory: Advances and Applications 287: 275-297 (2022-01-01)
Abstract (english): 
This chapter is devoted to the study of evolutionary inclusions. In contrast to evolutionary equations, we will replace the skew-selfadjoint operator A by a so-called maximal monotone relation A ⊆ H × H in the Hilbert space H. The resulting problem is then no longer an equation, but just an inclusion; that is, we consider problems of the form (u,f)∈∂t,νM(∂t,ν)+A¯, (u,f)∈ ∂ t,ν M(∂ t,ν )+A, where f∈ L2,ν(ℝ; H) is given and u∈ L2,ν(ℝ; H) is to be determined. This generalisation allows the treatment of certain non-linear problems, since we will not require any linearity for the relation A. Moreover, the property that A is just a relation and not neccessarily an operator can be used to treat hysteresis phenomena, which for instance occur in the theory of elasticity and electro-magnetism.
DOI: 10.15480/882.4183
ISBN: 978-3-030-89397-2
Institute: Mathematik E-10 
Document Type: Chapter (Book)
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
Part of Series: Operator theory 
Volume number: 287
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