Semiflow selection and Markov selection theorems

Autor:	Cardona, Jorge E., Kapitanski, Lev
Rok vydání:	2017
Předmět:	Mathematics - Dynamical Systems Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs Mathematics - Optimization and Control Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential equation are unique, and leads to a semiflow. We prove an abstract result on measurable selection of a semiflow for the situations without uniqueness. We outline applications to ODEs, PDEs, differential inclusions, etc. Our proof of the semiflow selection theorem is motivated by N. V. Krylov's Markov selection theorem. To accentuate this connection, we include a new version of the Markov selection theorem related to more recent papers of Flandoli & Romito and Goldys et al. Comment: In this revised version we have added a new abstract result in Sec. 2. It is used to correct the Navier-Stokes example in applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1707.04778 Zobrazit plný text záznamu View this record from Arxiv