Well-posedness and causality for a class of evolutionary inclusions

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.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Technische Universität Dresden

Year

2011

Author dc:creator

• Trostorff, Sascha

Contributors dc:contributor

• Picard, Rainer
• Milani, Albert

• Partielle Differentialgleichungen
• Monotone Operatoren
• Differentialinklusionen
• Evolutionäre Gleichungen
• Partial differential equations
• monotone operators
• differential inclusions
• evolutionary equations