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Transactions of the American Mathematical Society

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Radiation fields for semilinear wave equations

Authors: Dean Baskin and Antônio Sá Barreto
Journal: Trans. Amer. Math. Soc. 367 (2015), 3873-3900
MSC (2010): Primary 35L05
Published electronically: February 19, 2015
MathSciNet review: 3324913
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Abstract: We define the radiation fields of solutions to critical semilinear wave equations in $ \mathbb{R}^3$ and use them to define the scattering operator. We also prove a support theorem for the radiation fields with radial initial data. This extends the well-known support theorem for the Radon transform to this setting and can also be interpreted as a Paley-Wiener theorem for the distorted nonlinear Fourier transform of radial functions.

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Additional Information

Dean Baskin
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77840

Antônio Sá Barreto
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395

Received by editor(s): August 20, 2012
Received by editor(s) in revised form: December 19, 2012
Published electronically: February 19, 2015
Additional Notes: Both authors gratefully acknowledge NSF support. The first author was supported by postdoctoral fellowship DMS-1103436 and the second author by grant DMS-0901334. We would like to thank Rafe Mazzeo for fruitful discussions
Article copyright: © Copyright 2015 American Mathematical Society