Compactness for nonlinear transport equations

TL;DR

This paper establishes the existence of solutions for a class of nonlinear transport equations by proving their compactness, using a novel method that provides quantitative estimates applicable to both linear transport and scalar conservation laws.

Contribution

Introduces a new method that yields quantitative compactness estimates for nonlinear transport equations, bridging linear transport and scalar conservation law frameworks.

Findings

Proves compactness and existence of solutions for nonlinear transport equations.

Develops a new method for quantitative compactness estimates.

Applicable to models combining features of linear transport and scalar conservation laws.

Abstract

We prove compactness and hence existence for solutions to a class of non linear transport equations. The corresponding models combine the features of linear transport equations and scalar conservation laws. We introduce a new method which gives quantitative compactness estimates compatible with both frameworks.