On a certain type of nonlinear hyperbolic equations derived from astrophysical problems

TL;DR

This paper studies a specific class of nonlinear hyperbolic equations arising from astrophysics, focusing on boundary singularities and employing the Nash-Moser technique for analysis.

Contribution

It provides a unified abstract framework for analyzing nonlinear hyperbolic equations with boundary singularities in astrophysical models.

Findings

Application of Nash-Moser technique to boundary singularities

Unified treatment of equations from astrophysical problems

Insights into the regularity loss at boundary singularities

Abstract

Investigations of spherically symmetric motions of self-gravitating gaseous stars governed by the non-relativistic Newtonian gravitation theory or by the general relativistic theory lead us to a certain type of non-linear hyperbolic equations defined on a finite interval of the space variable. The linearized principal part has regular singularities at the both ends of the interval of the space variable. But the regularity loss caused by the singularities at the boundaries requires application of the Nash-Moser technique. An abstract unified treatment of the problem is presented.