DOAJ Open Access 2020

A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION

JOSÉ A. CARRILLO KATRIN GRUNERT HELGE HOLDEN

Abstrak

We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of the solution itself. In order to obtain uniqueness, one is required to augment the equation itself by a measure that represents the associated energy, and the breakdown of the solution is associated with a complicated interplay where the measure becomes singular. The main result in this paper is the construction of a Lipschitz metric that compares two solutions of the CH equation with the respective initial data. The Lipschitz metric is based on the use of the Wasserstein metric.

Topik & Kata Kunci

Mathematics

Penulis (3)

JOSÉ A. CARRILLO

KATRIN GRUNERT

HELGE HOLDEN

Format Sitasi

APA MLA BibTeX

CARRILLO, J.A., GRUNERT, K., HOLDEN, H. (2020). A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION. https://doi.org/10.1017/fms.2020.22

Akses Cepat

PDF tidak tersedia langsung

Cek di sumber asli →

Lihat di Sumber doi.org/10.1017/fms.2020.22

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.1017/fms.2020.22
Akses: Open Access ✓