Of concern are the properties of solutions of one space dimensional evolution equation utx,t=A u˙,t x,x∈ R,t>0, 0.1 where A is a nonlinear operator which is independent of the time t, maps functions of space variable · to functions of x. Examples of this include some important models such as Allen-Cahn equation, Neural network model and Ising model etc. We show that under certain assumptions on A , the solution of the rescaled version of (0.1) utx,t=A ue˙, t xe ,e>0small, will develop a 'transition layer structure', i.e. a pattern, at a predictable time and that this pattern will last for a very long time but will be eventually destroyed / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_25849 |
| Date | January 2002 |
| Contributors | Zhang, Zhenbu (Author), Wang, Xuefeng (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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