On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space
Sufficient conditions are found for the correct and unique solvability of a class of third-order parabolic operator differential equations, whose principal parts have multiple characteristics, in a Sobolev-type space with exponential weight. The estimates for the norms of intermediate derivative ope...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/2932134 |
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| _version_ | 1832545884050554880 |
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| author | Araz R. Aliev Sabir S. Mirzoev Mustafa A. Soylemezo |
| author_facet | Araz R. Aliev Sabir S. Mirzoev Mustafa A. Soylemezo |
| author_sort | Araz R. Aliev |
| collection | DOAJ |
| description | Sufficient conditions are found for the correct and unique solvability of a class of third-order parabolic operator differential equations, whose principal parts have multiple characteristics, in a Sobolev-type space with exponential weight. The estimates for the norms of intermediate derivative operators are obtained and the relationship between these estimates and solvability conditions is established. Besides, the connection is found between the order of exponential weight and the lower bound for the spectrum of abstract operator appearing in the principal part of the equation. |
| format | Article |
| id | doaj-art-da3d15ebb26b47499eaf8c41bf14bb62 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-da3d15ebb26b47499eaf8c41bf14bb622025-02-03T07:24:33ZengWileyJournal of Function Spaces2314-88962314-88882017-01-01201710.1155/2017/29321342932134On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted SpaceAraz R. Aliev0Sabir S. Mirzoev1Mustafa A. Soylemezo2Azerbaijan State Oil and Industry University, 1010 Baku, AzerbaijanInstitute of Mathematics and Mechanics of ANAS, 1141 Baku, AzerbaijanBaku Engineering University, Khirdalan City, 0101 Baku, AzerbaijanSufficient conditions are found for the correct and unique solvability of a class of third-order parabolic operator differential equations, whose principal parts have multiple characteristics, in a Sobolev-type space with exponential weight. The estimates for the norms of intermediate derivative operators are obtained and the relationship between these estimates and solvability conditions is established. Besides, the connection is found between the order of exponential weight and the lower bound for the spectrum of abstract operator appearing in the principal part of the equation.http://dx.doi.org/10.1155/2017/2932134 |
| spellingShingle | Araz R. Aliev Sabir S. Mirzoev Mustafa A. Soylemezo On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space Journal of Function Spaces |
| title | On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space |
| title_full | On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space |
| title_fullStr | On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space |
| title_full_unstemmed | On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space |
| title_short | On Solvability of Third-Order Operator Differential Equation with Parabolic Principal Part in Weighted Space |
| title_sort | on solvability of third order operator differential equation with parabolic principal part in weighted space |
| url | http://dx.doi.org/10.1155/2017/2932134 |
| work_keys_str_mv | AT arazraliev onsolvabilityofthirdorderoperatordifferentialequationwithparabolicprincipalpartinweightedspace AT sabirsmirzoev onsolvabilityofthirdorderoperatordifferentialequationwithparabolicprincipalpartinweightedspace AT mustafaasoylemezo onsolvabilityofthirdorderoperatordifferentialequationwithparabolicprincipalpartinweightedspace |