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| Title: | Some results on scattering for log-subcritical and log-supercritical nonlinear wave equations |
| Authors: | Shih, Hsi-Wei |
| Keywords: | Partial differential equation
Scattering theory
Wave equations
Mathematics |
| Issue Date: | Jul-2012 |
| Abstract: | We consider here two problems in the asymptotic behavior of semilinear second order
wave equations.
First, we consider the _H 1
x L2
x scattering theory for the energy log-subcritical wave
equation
2u = juj4ug(juj)
in R1+3, where g has logarithmic growth at 0. We discuss the solution with general
(resp. spherically symmetric) initial data in the logarithmically weighted (resp. lower
regularity) Sobolev space. We include also some observation about scattering in the
energy subcritical case.
The second problem studied here involves the energy log-supercritical wave equation
2u = juj4u log (2 + juj2); for 0 <
4
3
in R1+3. We prove the same results of global existence and ( _H 1
x\ _H2
x)H1
x scattering
for the equation with a slightly higher power of the logarithm factor in the nonlinearity
than that allowed by [26]. |
| Description: | University of Minnesota Ph.D. dissertation. July 2012. Major: Mathematics. Advisor: Markus Keel. 1 computer file (PDF); ii, 45 pages, appendix p. 35-36. |
| Permanent URL: | http://purl.umn.edu/135601 |
| Appears in Collections: | Dissertations
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Files in This Item:
| File |
Description |
Size | Format |
|---|
| Shih_umn_0130E_12984.pdf | | 508Kb | PDF | View/Open |
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