Philip Rosenau introduced the equation $u\sb{t} + (u + u\sp2)\sb{x} + u\sb{xxxxt} = 0,$ which models approximately the dynamics of certain large discrete systems. We study the Rosenau equation with initial and boundary conditions. First we establish global existence and uniqueness of solutions to the mixed problem for the generalized one dimensional Rosenau equation. Secondly we establish global existence and uniqueness in higher dimensional spaces. Then we study qualitative properties of the solutions, considering the initial value problem for the generalized one dimensional Rosenau equation. Of particular concern are pointwise decay estimates / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_23442 |
| Date | January 1990 |
| Contributors | Park, Mi Ai (Author), Goldstein, J. A (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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