| Autor: |
Myron K. Grammatikopoulos, Tzvetan D. Hristov, Nedyu I. Popivanov |
| Jazyk: |
angličtina |
| Rok vydání: |
2001 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Differential Equations, Vol 2001, Iss 01, Pp 1-26 (2001) |
| Druh dokumentu: |
article |
| ISSN: |
1072-6691 |
| Popis: |
In this paper we study boundary-value problems for the wave equation, which are three-dimensional analogue of Darboux-problems (or of Cauchy-Goursat problems) on the plane. It is shown that for $n$ in $mathbb{N}$ there exists a right hand side smooth function from $C^n(ar{Omega}_{0})$, for which the corresponding unique generalized solution belongs to $C^n(ar{Omega}_{0}ackslash O)$, and it has a strong power-type singularity at the point $O$. This singularity is isolated at the vertex $O$ of the characteristic cone and does not propagate along the cone. In this paper we investigate the behavior of the singular solutions at the point $O$. Also, we study more general boundary-value problems and find that there exist an infinite number of smooth right-hand side functions for which the corresponding unique generalized solutions are singular. Some a priori estimates are also stated. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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