Radiation fields for semilinear wave equations

Baskin, Dean; Sá Barreto, Antônio

doi:10.1090/S0002-9947-2015-06061-9

Radiation fields for semilinear wave equations
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by Dean Baskin and Antônio Sá Barreto PDF

Trans. Amer. Math. Soc. 367 (2015), 3873-3900 Request permission

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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