One method to prove of existence weak solution of a mixed problem for 2D parabolic equations
In this study using the residue method the solution of the first type mixed problem for 2D linear parabolic equation in the bounded cylinder of the Euclidean space R3(x,y,t)is obtained in explicit form. When the smoothness of initial data does not permit to construct of the classical solution then i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-09-01
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| Series: | Partial Differential Equations in Applied Mathematics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818120300024 |
| _version_ | 1819140453086265344 |
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| author | Bahaddin Sinsoysal Mahir Rasulov |
| author_facet | Bahaddin Sinsoysal Mahir Rasulov |
| author_sort | Bahaddin Sinsoysal |
| collection | DOAJ |
| description | In this study using the residue method the solution of the first type mixed problem for 2D linear parabolic equation in the bounded cylinder of the Euclidean space R3(x,y,t)is obtained in explicit form. When the smoothness of initial data does not permit to construct of the classical solution then it is necessary to extend the concept of classical solution. Based on the examined problem is proved that the obtained solution is a weak solution too. The use of this proof method to prove the existence of a weak solution can be applied to prove the existence of weak solutions for the more general problem with non-self-adjoint and even that contains higher-order derivative with respect to t in the boundary condition. |
| first_indexed | 2024-12-22T11:38:48Z |
| format | Article |
| id | doaj.art-215e96034ad642aea6252b29a4476d6e |
| institution | Directory Open Access Journal |
| issn | 2666-8181 |
| language | English |
| last_indexed | 2024-12-22T11:38:48Z |
| publishDate | 2020-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj.art-215e96034ad642aea6252b29a4476d6e2022-12-21T18:27:21ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812020-09-011100002One method to prove of existence weak solution of a mixed problem for 2D parabolic equationsBahaddin Sinsoysal0Mahir Rasulov1Beykent University, Department of Management Information Systems, Istanbul, Turkey; Corresponding author.Baku State University, Department of Numerical Methods of Mathematics, and Azerbaijan National Academy of Sciences, Institute of Oil and Gas, Department of Hydrogasdynamics of Reservoirs Systems, Baku, AzerbaijanIn this study using the residue method the solution of the first type mixed problem for 2D linear parabolic equation in the bounded cylinder of the Euclidean space R3(x,y,t)is obtained in explicit form. When the smoothness of initial data does not permit to construct of the classical solution then it is necessary to extend the concept of classical solution. Based on the examined problem is proved that the obtained solution is a weak solution too. The use of this proof method to prove the existence of a weak solution can be applied to prove the existence of weak solutions for the more general problem with non-self-adjoint and even that contains higher-order derivative with respect to t in the boundary condition.http://www.sciencedirect.com/science/article/pii/S2666818120300024Residue methodExpansion formulaWeak solution |
| spellingShingle | Bahaddin Sinsoysal Mahir Rasulov One method to prove of existence weak solution of a mixed problem for 2D parabolic equations Partial Differential Equations in Applied Mathematics Residue method Expansion formula Weak solution |
| title | One method to prove of existence weak solution of a mixed problem for 2D parabolic equations |
| title_full | One method to prove of existence weak solution of a mixed problem for 2D parabolic equations |
| title_fullStr | One method to prove of existence weak solution of a mixed problem for 2D parabolic equations |
| title_full_unstemmed | One method to prove of existence weak solution of a mixed problem for 2D parabolic equations |
| title_short | One method to prove of existence weak solution of a mixed problem for 2D parabolic equations |
| title_sort | one method to prove of existence weak solution of a mixed problem for 2d parabolic equations |
| topic | Residue method Expansion formula Weak solution |
| url | http://www.sciencedirect.com/science/article/pii/S2666818120300024 |
| work_keys_str_mv | AT bahaddinsinsoysal onemethodtoproveofexistenceweaksolutionofamixedproblemfor2dparabolicequations AT mahirrasulov onemethodtoproveofexistenceweaksolutionofamixedproblemfor2dparabolicequations |