Singular solutions for the Uehling-Uhlenbeck equation
Miguel Escobedo, Stephane Mischler, and Juan J.L. Velazquez
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Submission date: 24. Jan. 2007
published in: Proceedings of the Royal Society of Edinburgh / A, 138 (2008) 1, p. 67-107
DOI number (of the published article): 10.1017/S0308210506000655
MSC-Numbers: 35Q40, 82C10
Keywords and phrases: kinetic equation, singular solutions
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In this paper we prove the existence of solutions of the Uehling-Uhlenbeck equation that behave like k^(-7/6) as k tends to zero. From the physical point of view, such solutions can be thought as particle distributions in the space of momentum having a sink (or a source) of particles with zero momentum. Our construction is based on the precise estimates of the semigroup for the linearized equation around the singular function k^(-7/6) that we obtained in .