dc.contributor.author Cortés, E. dc.date.accessioned 2018-12-19T15:01:14Z dc.date.available 2018-12-19T15:01:14Z dc.date.issued 2018-12-19 dc.identifier.uri http://hdl.handle.net/20.500.11824/904 dc.description.abstract In this thesis, we present a mathematical study of three problems arising in the kinetic theory of quantum gases. en_US In the first part, we consider a Boltzmann equation that is used to describe the time evolution of the particle density of a homogeneous and isotropic photon gas, that interacts through Compton scattering with a low-density electron gas at non-relativistic equilibrium. The kernel in the kinetic equation is highly singular, and we introduce a truncation motivated by the very-peaked shape of the kernel along the diagonal. With this modified kernel, the global existence of measure-valued weak solutions is established for a large set of initial data. We also study a simplified version of this equation, that appears at very low temperatures of the electron gas, where only the quadratic terms are kept. The global existence of measure-valued weak solutions is proved for a large set of initial data, as well as the global existence of $L^1$ solutions for initial data that satisfy a strong integrability condition near the origin. The long time asymptotic behavior of weak solutions for this simplified equation is also described. In the second part of the thesis, we consider a system of two coupled kinetic equations related to a simplified model for the time evolution of the particle density of the normal and superfluid components in a homogeneous and isotropic weakly interacting dilute Bose gas. We establish the global existence of measure-valued weak solutions for a large class of initial data. The conservation of mass and energy and the production of moments of all positive order is also proved. Finally, we study some of the properties of the condensate density and establish an integral equation that describes its time evolution. dc.description.sponsorship MTM2014-52347-C2-1-R of DGES en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title Measure-valued weak solutions to some kinetic equations with singular kernels for quantum particles en_US dc.type info:eu-repo/semantics/article en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US
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