| Autor: |
Yolanda Santiago Ayala, Santiago Rojas Romero |
| Jazyk: |
Spanish; Castilian |
| Rok vydání: |
2020 |
| Předmět: |
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| Zdroj: |
Selecciones Matemáticas, Vol 7, Iss 01, Pp 52-73 (2020) |
| Druh dokumentu: |
article |
| ISSN: |
2411-1783 |
| DOI: |
10.17268/sel.mat.2020.01.06 |
| Popis: |
In this article, we first prove that the initial value problem associated to the homogeneous wave equation in periodic Sobolev spaces has a global solution and the solution has continuous dependence with respect to the initial data, in [0; T], T > 0. We do this in an intuitive way using Fourier theory and in a fine version introducing families of strongly continuous operators, inspired by the works of Iorio [4] and Santiago and Rojas [7]. Also, we prove that the energy associated to the wave equation is conservative in intervals [0; T], T > 0. As a final result, we prove that the initial value problem associated to the non homogeneous wave equation has a local solution and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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