English

Global existence for a class of viscous systems of conservation laws

Analysis of PDEs 2019-08-20 v3

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.

Keywords

Cite

@article{arxiv.1902.02714,
  title  = {Global existence for a class of viscous systems of conservation laws},
  author = {Luca Alasio and Stefano Marchesani},
  journal= {arXiv preprint arXiv:1902.02714},
  year   = {2019}
}