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Inverse scattering for critical semilinear wave equations

Antônio Sá Barreto, Gunther Uhlmann and Yiran Wang

Vol. 4 (2022), No. 2, 191–223
DOI: 10.2140/paa.2022.4.191
Abstract

We show that the scattering operator for defocusing energy critical semilinear wave equations u + f(u) = 0, f C() and f u5, in three space dimensions, determines f.

Keywords
nonlinear wave equations, radiation fields, scattering, inverse scattering
Mathematical Subject Classification
Primary: 35P25, 58J50, 35R30
Milestones
Received: 19 January 2021
Accepted: 5 January 2022
Published: 16 October 2022
Authors
Antônio Sá Barreto
Department of Mathematics
Purdue University
West Lafayette, IN
United States
Gunther Uhlmann
Department of Mathematics
University of Washington
Seattle, WA
United States
Institute for Advanced Study
Hong Kong University of Science and Technology
Clear Water Bay
Hong Kong
Yiran Wang
Department of Mathematics
Emory University
Atlanta, GA
United States