Заглавие | ESTIMATES FOR THE SINGULAR SOLUTIONS OF THE 3-D PROTTER’S PROBLEM |
Вид публикация | Journal Article |
Година на публикуване | 2004 |
Автори | Popivanov N, Popov T |
Списание | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Том | 96 |
ключови думи | boundary value problems, generalized solution, propagation of singularities, singular solutions, special functions, wave equation |
Резюме | For the wave equation we study boundary value problems, stated by Protter in 1952, as some three-dimensional analogues of Darboux problems on the plane. It is known that Protter's problems are not well posed and the solution may have singularity at the vertex $O$ of a characteristic cone, which is a part of the domain's boundary $\partial \Omega $. It is shown that for $n$ in $\mathbb{N}$ there exists a right-hand side smooth function from $C^{n}(\bar{\Omega})$, for which the corresponding unique generalized solution belongs to $C^{n}(\bar{\Omega}\backslash O)$, but it has a strong power-type singularity. It is isolated at the vertex $O$ and does not propagate along the cone. The present article gives some necessary and sufficient conditions for the existence of a fixed order singularity. It states some exact a priori estimates for the solution. |
2000 MSC | main 35L05, 35L20, 35D05, 35A20, secondary 33C05, 33C90 |
Прикачен файл | Размер |
---|---|
1296.pdf | 34.41 KB |
Прикачен файл | Размер |
---|---|
96-117-139.pdf | 1.61 MB |