The method of steepest descent is used to solve partial differential equations of mixed type. In the main hypothesis for this paper, H, L, and S are Hilbert spaces, T: H -> L and B: H -> S are functions with locally Lipshitz Fréchet derivatives where T represents a differential equation and B represents a boundary condition. Define ∅(u) = 1/2 II T(u) II^2. Steepest descent is applied to the functional ∅. A new smoothing technique is developed and applied to Tricomi type equations (which are of mixed type). Finally, the graphical outputs on some test boundary conditions are presented in the table of illustrations.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc332800 |
| Date | 08 1900 |
| Creators | Kim, Keehwan |
| Contributors | Neuberger, John W., Warchall, Henry A., Renka, Robert J. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | v, 74 leaves : ill., Text |
| Rights | Public, Kim, Keehwan, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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