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1	Limiting Processes in Evolutionary Equations - A Hilbert Space Approach to Homogenization Waurick, Marcus 21 April 2011 (has links) (PDF) In a Hilbert space setting homogenization of evolutionary equations is discussed. In order to do so, a suitable topology on material laws is introduced and several properties of that topology are shown. With those properties homogenization theorems of a large class of linear evolutionary problems of classical mathematical physics can be obtained. The results are exemplified by the equations of piezo-electro-magnetism. Homogenisierung Partielle Differentialgleichungen Evolutionsgleichungen Homogenization Partial Differential Equations Evolution Equations ddc:510 rvk:SK 540
2	Well-posedness and causality for a class of evolutionary inclusions Trostorff, Sascha 05 December 2011 (has links) (PDF) 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. Partielle Differentialgleichungen Monotone Operatoren Differentialinklusionen Evolutionäre Gleichungen Partial differential equations monotone operators differential inclusions evolutionary equations ddc:510 rvk:SK 540
3	Exponential Stability and Initial Value Problems for Evolutionary Equations Trostorff, Sascha 31 May 2018 (has links) (PDF) The thesis deals with so-called evolutionary equations, a class of abstract linear operator equations, which cover a huge class of partial differential equation with and without memory. We provide a unified Hilbert space framework for the well-posedness of such equations. Moreover, we inspect the exponential stability of those problems and construct spaces of admissible inital values and pre-histories, on which a strongly continuous semigroup could be associated with the given problem. The theoretical results are illustrated by several examples. Partielle Differentialgleichungen Wohlgestelltheit Exponentielle Stabilität Anfangswerte und Vorgeschichten Delay Gleichungen Integro-Differentialgleichungen partial differential equations well-posedness exponential stability initial values and pre-histories delay equations integro-differential equations ddc:510 rvk:SK 540

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