# The Ostrovsky Hunter equation with a space dependent flux function

## TL;DR

This paper investigates the periodic Ostrovsky-Hunter equation with a spatially dependent flux, establishing existence, uniqueness, and convergence of entropy solutions via finite volume schemes with a specific convergence rate.

## Contribution

It proves the existence and uniqueness of entropy solutions for the spatially dependent flux case and demonstrates convergence of finite volume approximations at rate 1/2.

## Key findings

- Existence and uniqueness of entropy solutions for the equation.
- Finite volume scheme converges to the entropy solution at rate 1/2.
- The flux function's regularity is crucial for the analysis.

## Abstract

We study the periodic Ostrovsky-Hunter equation in the case where the flux function may depend on the spatial variable. Our main results are that if the flux function is twice differentiable, then there exists a unique entropy solution. This entropy solution may be constructed as a limit of approximate solutions generated by a finite volume scheme, and the finite volume approximations converge to the entropy solution at a rate 1/2.