Existence and uniqueness of solutions to the steady boltzmann equation

Simple item page
dc.contributor.authorGhomeshi, Shahinen_US
dc.date.accessioned2024-08-13T22:54:25Z
dc.date.available2024-08-13T22:54:25Z
dc.date.copyright1998en_US
dc.date.issued1998
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractIn this thesis our main objective is to prove the existence and uniqueness of solutions to the Steady Boltzmann Equation with inflow and diffusive boundary conditions, without truncations of the collision kernel. Due to the singularity at v = 0, the non-linear term in the Steady Boltzmann Equation becomes significantly large. In addition to this, another problem with proving existence of steady solutions is that the collision term becomes unbounded as v -> ∞ for hard-sphere interactions. Previous authors have attacked these problems by imposing unphysical trunca­tions on the collision kernel so that collisions between particles having small veloc­ities are ignored. An additional truncation is then made to control the magnitude of the velocities so that it will not grow without bound. We present and detail some of the work of Maslova and show that the colli­sion operator has the properties which make it possible to avoid truncations. We introduce several properties of the collision operator which include a series of cru­cial estimates. These estimates are later used to produce function spaces with the contractive property. General existence and uniqueness is then obtained by an ap­plication of the Contraction Mapping Principle.
dc.format.extent107 pages
dc.identifier.urihttps://hdl.handle.net/1828/17902
dc.rightsAvailable to the World Wide Weben_US
dc.titleExistence and uniqueness of solutions to the steady boltzmann equationen_US
dc.typeThesisen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
GHOMESHI_Shahin_MSC_1998_941861.pdf
Size:
10.72 MB
Format:
Adobe Portable Document Format
Download

Collections

Electronic Theses and Dissertations (ETD)
 
University of Victoria Libraries

We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.