Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
7/2007

Singular solutions for the Uehling-Uhlenbeck equation

Miguel Escobedo, Stephane Mischler and Juan J.L. Velazquez

Abstract

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 [5].

Received:
Jan 24, 2007
Published:
Jan 24, 2007
MSC Codes:
35Q40, 82C10
Keywords:
kinetic equation, singular solutions

Related publications

inJournal
2008 Repository Open Access
M. Escobedo, S. Mischler and Juan J. L. Velázquez

Singular solutions for the Uehling-Uhlenbeck equation

In: Proceedings of the Royal Society of Edinburgh / A, 138 (2008) 1, pp. 67-107