New distributional global solutions for the Hunter-Saxton equation
type: Item
instance of: scholarly article
title: New distributional global solutions for the Hunter-Saxton equation
zbMATH Open document ID: 1474.35571
DOI: 10.1155/2014/809095
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: In the setting of a distributional product, we consider a Riemann problem for the Hunter-Saxton equation \([u_t +((1 / 2) u^2)_x]_x = (1 / 2) u_x^2\) in a convenient space of discontinuous functions. With the help of a consistent extension of the classical solution concept, two classes of discontinuous solutions are obtained: one class of conservative solutions and another of dispersive solutions. A necessary and sufficient condition for the propagation of a distributional profile as a travelling wave is also presented, which allows identifying an interesting set of explicit distributional travelling waves. In the paper, we will show some results we have obtained by applying this framework to other equations and systems.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 76A15
zbMATH DE Number: 7023117
Wikidata QID: Q59041682
author: Carlos Orlando R. Sarrico
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/809095
OpenAlex ID: W2057197709
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description: scientific article; zbMATH DE number 7023117