Asymptotic completeness for a scalar quasilinear wave equation satisfying the weak null condition / Dongxiao Yu.

Format:

Book

Author/Creator:

Yu, Dongxiao (Researcher in partial differential equations), author.

Series:

Memoirs of the American Mathematical Society ; no. 1492.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1492

Language:

English

Subjects (All):

Mathematical analysis.

Differential equations, Partial.

Physical Description:

v, 128 pages ; 26 cm

Place of Publication:

Providence, RI : American Mathematical Society, 2024.

Summary:

In this paper, we prove the first asymptotic completeness result for a scalar quasilinear wave equation satisfying the weak null condition. The main tool we use in the study of this equation is the geometric reduced system introduced in Yu (Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition, 2021). Starting from a global solution u to the quasilinear wave equation, we rigorously show that well chosen asymptotic variables solve the same reduced system with small error terms. This allows us to recover the scattering data for our system, as well as to construct a matching exact solution to the reduced system.

Contents:

Chapter 1. Introduction

Chapter 2. Preliminaries

Chapter 3. Construction of the optical function

Chapter 4. Derivatives of the optical function

Chapter 5. The asymptotic equations and the scattering data

Chapter 6. Gauge independence

Chapter 7. Approximation

Bibliography.

Notes:

Includes bibliographical references (pages 127-128).

ISBN:

1470470489

9781470470487

OCLC:

1449623946