Singularities generated by the triple interaction of semilinear conormal waves

Sá Barreto, Antônio; Wang, Yiran

doi:10.2140/apde.2021.14.135

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1948-206X (e-only)

ISSN: 2157-5045 (print)

Author Index

To Appear

Other MSP Journals

This article is available for purchase or by subscription. See below.

Singularities generated by the triple interaction of semilinear conormal waves

Antônio Sá Barreto and Yiran Wang

Vol. 14 (2021), No. 1, 135–170

DOI: 10.2140/apde.2021.14.135

Abstract

We study the local propagation of conormal singularities for solutions of semilinear wave equations $□ u = P (y, u)$ , where $P (y, u)$ is a polynomial of degree $N \geq 3$ in $u$ with $C^{\infty} (ℝ_{y}^{3})$ coefficients. We know from the work of Melrose and Ritter and Bony that if $u$ is conormal to three waves which intersect transversally at point $q$ , then after the triple interaction $u (y)$ is a conormal distribution with respect to the three waves and the characteristic cone $𝒬$ with vertex at $q$ . We compute the principal symbol of $u$ at the cone and away from the hypersurfaces. We show that if $\partial_{u}^{3} P (q, u (q)) \neq 0$ , then $u$ is an elliptic conormal distribution.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 18.207.133.27 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords

nonlinear wave equations, propagation of singularities, wave front sets, conformal distributions

Mathematical Subject Classification

Primary: 35A18, 35A21, 35L70

Milestones

Received: 26 October 2018

Revised: 31 July 2019

Accepted: 7 October 2019

Published: 19 February 2021

Authors

Antônio Sá Barreto
Department of Mathematics Purdue University West Lafayette, IN United States

Yiran Wang
Department of Mathematics Emory University Atlanta, GA United States

Vol. 14, No. 1, 2021