Dissertation
Problems in applied dispersive and parabolic partial differential equations
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2026
DOI:
https://doi.org/10.17918/00011445
Abstract
This thesis first explores the well-posedness issues of Benjamin-Ono equation with quasiperiodic initial data, which includes data of the form f(x) = f₁(x) + ... + f_N(x), where f_i is periodic with period [alpha]_i and the periods are rationally independent. By developing the classical tools, namely the energy method and an abstract Cauchy-Kowalevski theorem, we succeed in proving the local well-posedness in quasiperiodic Sobolev spaces as well as for quasiperiodic analytic datum. Our second objective is an investigation of coherent structures of two coordinate-free models of flame fronts, one linear and the other nonlinear in the curvature variable. By means of the classical Crandall-Rabinowitz bifurcation theorem, we prove existence of nontrivial families of vertically advancing flame fronts bifurcating from a zero solution.
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Details
- Title
- Problems in applied dispersive and parabolic partial differential equations
- Creators
- Sultan Aitzhan
- Contributors
- David M. Ambrose (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University
- Number of pages
- viii, 80 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991022189165504721