Existence Theory in Sobolev Spaces for an Aggregation Equation

Graduate Project

Public Deposited

Citeable URL: https://ir.library.oregonstate.edu/concern/graduate_projects/g732dh46b

Descriptions

Attribute Name	Values
Creator	Barta, Hannah E.
Abstract	Aggregation equations have been used to model phenomena such as insect swarming and chemotaxis. Previous work on aggregation equations in the area of analysis applied to PDE has proven well-posedness of certain classes of aggregation equations in Lebesgue spaces. We will prove local existence of solutions in H^1 to an aggregation equation with an acceptable potential. The existence proof requires several key estimates in Sobolev spaces, primarily the H^k spaces. It turns out that we can also guarantee global existence of solutions in H^1 for smoother potentials. This work is based on the research of Thomas Laurent.
Resource Type	Capstone Project
Date Issued	2021-06-08
Degree Level	Master's
Degree Name	Master of Science (M.S.)
Degree Field	Mathematics
Degree Grantor	Oregon State University
Commencement Year	2021
Advisor	Cozzi, Elaine
Committee Member	Thomann, Enrique Showalter, Ralph Higdon, Robert
Academic Affiliation	Mathematics
Rights Statement	In Copyright
Publisher	Oregon State University
Peer Reviewed	No
Language	English [eng]

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