Nonlinear waves and photon loss in the Kompaneets model of Compton scattering

Abstract: The Kompaneets equation is fundamental for explaining the Sunyaev-Zeldovich effect, which involves deformation of the cosmic microwave background energy spectrum due to Compton scattering of photons by electrons. We establish L1 convergence to Bose-Einstein equilibria in large time and prove several results on the existence and behavior of a `condensate' of photons at the zero-energy boundary. The Kompaneets equation is a scalar conservation law with a degenerate parabolic nature that permits a loss of photons in finite time due to shock formation at zero energy. Solutions satisfy entropy decay, an Oleinik one-sided slope bound, and L1 contraction and comparison principles.

mathematical physicsanalysis of PDEsclassical analysis and ODEscomplex variablesdynamical systemsfunctional analysisnumerical analysisspectral theory

Audience: researchers in the topic

Nonlinear Waves and Coherent Structures Webinar Series

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