DSpace DSpace

University of Minnesota Digital Conservancy >
University of Minnesota - Twin Cities >
Dissertations and Theses >
Dissertations >

Please use this identifier to cite or link to this item: http://hdl.handle.net/11299/135601

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
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.
URI: http://purl.umn.edu/135601
Appears in Collections:Dissertations

Files in This Item:

File Description SizeFormat
Shih_umn_0130E_12984.pdf508.72 kBPDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.