Dokuchaev, N.G. The integral estimations for ordinary differential equations with a discontinuity on a domain boundary

TL;DR

This paper investigates the regularity and estimation of solutions and first exit times for boundary-killed ODEs, providing new bounds and properties for solution densities under certain conditions.

Contribution

It introduces integral estimations for solutions of boundary-killed ODEs and analyzes the regularity of their densities, advancing understanding of boundary effects on solution behavior.

Findings

Established L2-norm estimates for solutions and exit times.

Derived regularity properties for solution densities with random initial conditions.

Provided bounds and properties relevant for boundary-killed ODE analysis.

Abstract

The paper studies solutions of ODEs killed on the domain boundary and their first exit times from the domain. Some regularity is obtained in the form of estimates of L_2-norm for functionals on solutions and the first exit times. Some regularity properties for the density of solutions killed on the boundary is also studied for the case of random initial conditions.