Non-Standard Analysis, Multiplication of Schwartz Distributions and Delta-Like Solution of Hopf's Equation
| dc.creator | Berger, Guy | |
| dc.date | 2008-09-25 | |
| dc.date | 2008-10-10 | |
| dc.date.accessioned | 2026-07-07T10:08:40Z | |
| dc.date.available | 2026-07-07T10:08:40Z | |
| dc.description | We construct an algebra of generalized functions $^*\mathcal{E}(\mathbb{R}^d)$. We also construct an embedding of the space of Schwartz distributions $\mathcal{D}^\prime(\mathbb{R}^d)$ into $^*\mathcal{E}(\mathbb{R}^d)$ and thus present a solution of the problem of multiplication of Schwartz distributions which improves J.F. Colombeau's solution. As an application we prove the existence of a weak delta-like solution in ${^*\mathcal{E}(\mathbb{R}^d)}$ of the Hopf equation. This solution does not have a counterpart in the classical theory of partial differential equations. Our result improves a similar result by M. Radyna obtained in the framework of perturbation theory. | |
| dc.description | This is a Master thesis of Guy Burger, under the supervision of Todor D. Todorov, defended in Mathematics Department of California Polytechnic State Universiy, San Luis Obispo, CA-93407, in Cal Poly Library, LD729.6.S 52 M3 B47, 2005 | |
| dc.identifier | https://arxiv.org/abs/0809.4322 | |
| dc.identifier | http://arxiv.org/abs/0809.4322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171074 | |
| dc.subject | Functional Analysis | |
| dc.subject | 26E35, 30G06, 46F30, 46F10, 46S10, 46S20, 35D05, 35L67, 35L65. | |
| dc.title | Non-Standard Analysis, Multiplication of Schwartz Distributions and Delta-Like Solution of Hopf's Equation | |
| dc.type | text |