# Global existence for a class of viscous systems of conservation laws

## TL;DR

This paper establishes the global existence and boundedness of classical solutions for a class of viscous conservation laws in one dimension, using advanced mathematical techniques and applicable to physical models of springs.

## Contribution

It extends existing results by applying Amann's criterion and entropy methods to systems with possibly degenerate diffusion, ensuring global solutions.

## Key findings

- Proves global existence of solutions for viscous conservation laws.
- Uses Amann's criterion and entropy methods for degenerate systems.
- Applicable to physical models of springs and material deformation.

## Abstract

We prove existence and boundedness of classical solutions for a family of viscous conservation laws in one space dimension for arbitrarily large time. The result relies on H. Amann's criterion for global existence of solutions and on suitable uniform-in-time estimates for the solution. We also apply J\"ungel's boundedness-by-entropy principle in order to obtain global existence for systems with possibly degenerate diffusion terms. This work is motivated by the study of a physical model for the space-time evolution of the strain and velocity of an anharmonic spring of finite length.