Global Lp solutions of the Boltzmann equation with an angle-potential concentrated collision kernel and convergence to a Landau solution

dc.contributor.advisorMartínez Gamba, Irene, 1957-
dc.contributor.committeeMemberVasseur, Alexis F
dc.contributor.committeeMemberCaffarelli, Luis A
dc.contributor.committeeMemberPavlovic, Natasa
dc.contributor.committeeMemberChen, Thomas
dc.contributor.committeeMemberRen, Kui
dc.contributor.committeeMemberMorrison, Phil J
dc.creatorAkopian, Sona
dc.creator.orcid0000-0002-4477-7714
dc.date.accessioned2017-12-19T15:27:48Z
dc.date.available2017-12-19T15:27:48Z
dc.date.created2017-05
dc.date.issued2017-05-05
dc.date.submittedMay 2017
dc.date.updated2017-12-19T15:27:48Z
dc.description.abstractWe solve the Cauchy problem associated to the space homogeneous Boltzmann equation with an angle-potential singular concentration modeling the collision kernel, proposed in 2013 by Bobylev and Potapenko. The potential under consideration ranges from Coulomb to hard spheres cases, however, the motivation of such a collision kernel is to treat the (extreme) case of Coulomb potentials, on which this particular form of collision operator is well defined. We show that the scaled angle-potential singular concentration in a grazing collisions limit makes the Boltzmann operator converge in the sense of distributions to the Landau operator acting on the Boltzmann solutions, and also that solutions of this type of Boltzmann equation converge to solutions of the Landau equation that conserve mass, momentum and energy.
dc.description.departmentMathematics
dc.format.mimetypeapplication/pdf
dc.identifierdoi:10.15781/T2B85410X
dc.identifier.urihttp://hdl.handle.net/2152/63030
dc.language.isoen
dc.subjectBoltzmann equation
dc.subjectLandau equation
dc.subjectGrazing collisions limit
dc.subjectCoulomb potentials
dc.subjectExistence theory
dc.titleGlobal Lp solutions of the Boltzmann equation with an angle-potential concentrated collision kernel and convergence to a Landau solution
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorThe University of Texas at Austin
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

Access full-text files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
AKOPIAN-DISSERTATION-2017.pdf
Size:
447.75 KB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 2 of 2
No Thumbnail Available
Name:
PROQUEST_LICENSE.txt
Size:
4.45 KB
Format:
Plain Text
Description:
No Thumbnail Available
Name:
LICENSE.txt
Size:
1.84 KB
Format:
Plain Text
Description: