We study a class of differential inclusions involving maximal monotone relations, which cover a huge class of problems in mathematical physics. For this purpose we introduce the time derivative as a continuously invertible operator in a suitable Hilbert space. It turns out that this realization is a strictly monotone operator and thus, the question on existence and uniqueness can be answered by well-known results in the theory of maximal monotone relations. Furthermore, we show that the resulting solution operator is Lipschitz-continuous and causal, which is a natural property of evolutionary processes. Finally, the results are applied to a system of partial differential equations and inclusions, which describes the diffusion of a compressible fluid through a saturated, porous, plastically deforming media, where certain hysteresis phenomena are modeled by maximal montone relations.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:14-qucosa-78325 |
| Date | 05 December 2011 |
| Creators | Trostorff, Sascha |
| Contributors | Technische Universität Dresden, Fakultät Mathematik und Naturwissenschaften, Prof. Dr. Rainer Picard, Prof. Dr. Rainer Picard, Prof. Dr. Albert Milani |
| Publisher | Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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