Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem
For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one p...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/260287 |
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| _version_ | 1832562137490259968 |
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| author | Nedyu Popivanov Todor Popov Allen Tesdall |
| author_facet | Nedyu Popivanov Todor Popov Allen Tesdall |
| author_sort | Nedyu Popivanov |
| collection | DOAJ |
| description | For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertex O of the boundary light characteristic cone and does not propagate along the bicharacteristics. The present paper describes asymptotic expansions of the generalized solutions in negative powers of the distance to O. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for the singular solutions are obtained. |
| format | Article |
| id | doaj-art-e5156add09eb475295e6e34d01855cb9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e5156add09eb475295e6e34d01855cb92025-02-03T01:23:22ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/260287260287Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz ProblemNedyu Popivanov0Todor Popov1Allen Tesdall2Department of Mathematics and Informatics, University of Sofia, 1164 Sofia, BulgariaDepartment of Mathematics and Informatics, University of Sofia, 1164 Sofia, BulgariaDepartment of Mathematics, City University of New York, College of Staten Island, Staten Island, NY 10314, USAFor the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertex O of the boundary light characteristic cone and does not propagate along the bicharacteristics. The present paper describes asymptotic expansions of the generalized solutions in negative powers of the distance to O. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for the singular solutions are obtained.http://dx.doi.org/10.1155/2014/260287 |
| spellingShingle | Nedyu Popivanov Todor Popov Allen Tesdall Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem Abstract and Applied Analysis |
| title | Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem |
| title_full | Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem |
| title_fullStr | Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem |
| title_full_unstemmed | Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem |
| title_short | Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem |
| title_sort | semi fredholm solvability in the framework of singular solutions for the 3 1 d protter morawetz problem |
| url | http://dx.doi.org/10.1155/2014/260287 |
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