In this study, we consider the generalized function solutions to nonlinear wave equation with distribution initial data. J. F. Colombeau shows that the initial value problem u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 then inspect the generalized function representatives for the initial value problem solution to see if the generalized function solution is a distribution or is more singular. Using the numerical technics, we show for specific F and specific distribution initial data u_0, u_1, there is no distribution solution.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc278853 |
| Date | 08 1900 |
| Creators | Kim, Jongchul |
| Contributors | Warchall, Henry Alexander, Neuberger, John W., Castro, Alfonso, 1950-, Iaia, Joseph 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, 53 leaves : ill., Text |
| Rights | Public, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved., Kim, Jongchul |
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