Dissertation/Thesis Abstract

Quasi-Variational Inequalities for Source-Expanding Hele-Shaw Problems
by DeIonno, John Adrian, Ph.D., University of California, Berkeley, 2013, 74; 3593813
Abstract (Summary)

We study nonlinear partial differential equations describing Hele-Shaw flows for which the source of the fluid, which classically is at a single point, instead expands as the moving boundary uncovers new sources. This problem is reformulated as a type of quasi-variational inequality, for which we show there exists a unique weak solution. Our procedure utilizes a Baiocchi integral transform. However, unlike in traditional applications, the inequality solved by the transformed variable continues to depend on the free boundary, and thus standard theory of variational inequalities cannot be immediately applied. Instead, we develop convergent time-stepping scheme. As a further application, we generalize and study a related problem with a growing density function obeying a hard constraint on the maximum density.

Indexing (document details)
Advisor: Evans, Lawrence C.
Commitee: Papadopoulos, Panayiotis, Wilkening, Jon
School: University of California, Berkeley
Department: Mathematics
School Location: United States -- California
Source: DAI-B 75/01(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Free boundary problems, Hard constraint, Hele-shaw flow, Moving boundary problem, Obstacle problem, Variational inequality
Publication Number: 3593813
ISBN: 978-1-303-37226-1
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