Geodesic
Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 200-206 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

Voir la notice de l'acte

Four-dimensional boundary value problems for the nonhomogeneous wave equation are studied. They were proposed by M. Protter as multidimensional analogues of Darboux problems in the plane. It is known that the unique generalized solution may have a strong power-type singularity at only one boundary point. This singularity is isolated at the vertex of the characteristic cone and does not propagate along the cone. Another aspect is that the problem is not Fredholm, since it has infinite-dimensional cokernel. Some known results suggest that the solution may have at most exponential growth, but the question whether such solutions really exist was still open. We show that the answer is positive and construct generalized solution of Protter problem with exponential singularity. *2000 Mathematics Subject Classification: 35L05, 35L20, 35D05, 35D10, 35C10.
Keywords: Boundary Value Problems, Generalized Solution, Semi-Fredholm Solvability, Special Functions, Wave Equation 
@incollection{MEM_2011_40_1_a18,
     author = {Popivanov, Nedyu and Popov, Todor and Scherer, Rudolf},
     title = {Singular {Solutions} with {Exponential} {Growth} for the {(3+1)-D} {Wave} {Equation}},
     booktitle = {},
     series = {Mathematics and Education in Mathematics},
     pages = {200--206},
     year = {2011},
     volume = {40},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a18/}
}
TY  - JOUR
AU  - Popivanov, Nedyu
AU  - Popov, Todor
AU  - Scherer, Rudolf
TI  - Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation
JO  - Mathematics and Education in Mathematics
PY  - 2011
SP  - 200
EP  - 206
VL  - 40
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a18/
LA  - en
ID  - MEM_2011_40_1_a18
ER  - 
%0 Journal Article
%A Popivanov, Nedyu
%A Popov, Todor
%A Scherer, Rudolf
%T Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation
%J Mathematics and Education in Mathematics
%D 2011
%P 200-206
%V 40
%N 1
%U http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a18/
%G en
%F MEM_2011_40_1_a18
Popivanov, Nedyu; Popov, Todor; Scherer, Rudolf. Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 200-206. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a18/