Irregular dynamic systems according to R.J. DiPerna and P.L. Lions
Alexander Ovseevich
TL;DR
This paper reviews the concept of generalized solutions to singular ordinary differential equations, emphasizing their significance in understanding irregular dynamic systems and extending the foundational work of DiPerna and Lions.
Contribution
It extends and simplifies the original DiPerna-Lions approach to generalized solutions of singular ODEs and discusses further extensions of the theory.
Findings
Clarification of generalized solution concepts
Simplified approach to singular ODEs
Discussion of further theoretical extensions
Abstract
These are notes of a seminar held at the Institute for Problems in Mechanics, RAS in 2003 and aimed at presentation of [R.J. DiPerna and P.L. Lions, Invent. math. 98, 511 (1989)]. We discuss the notion of a generalized solution to a singular Ordinary Differential Equation introduced by DiPerna and Lions. We stress importance of singular dynamic systems from the "philosophia naturalis" point of view, and extend and simplify the original approach by R.J. DiPerna and P.L. Lions. Further extensions are discussed.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Numerical methods for differential equations · Dynamics and Control of Mechanical Systems