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dc.contributor.advisorGomes, Diogo A.
dc.contributor.authorBerkemeier, Francisco
dc.date.accessioned2018-05-14T05:49:34Z
dc.date.available2018-05-14T05:49:34Z
dc.date.issued2018-05-13
dc.identifier.doi10.25781/KAUST-TI27W
dc.identifier.urihttp://hdl.handle.net/10754/627833
dc.description.abstractIn this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the heat equation by estimating the decay of Lebesgue norms. Then, we apply similar methods to the Fokker-Planck equation with suitable assumptions on the advection and diffusion. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. The main contribution of this thesis is the use of functional inequalities to express decay of norms as differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.
dc.language.isoen
dc.subjectPDE
dc.subjectregularity
dc.subjectparabolic
dc.subjectestimates
dc.titleA Priori Regularity of Parabolic Partial Differential Equations
dc.typeThesis
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberTzavaras, Athanasios
dc.contributor.committeememberSantamarina, Carlos
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameMaster of Science
refterms.dateFOA2018-06-13T19:02:18Z


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