Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay
The first boundary-value problem for an autonomous second-order system of linear partial differential equations of parabolic type with a single delay is considered. Assuming that a decomposition of the given system into a system of independent scalar second-order linear partial differential equation...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/219040 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558068808810496 |
|---|---|
| author | Josef Diblík Denis Khusainov Oleksandra Kukharenko Zdeněk Svoboda |
| author_facet | Josef Diblík Denis Khusainov Oleksandra Kukharenko Zdeněk Svoboda |
| author_sort | Josef Diblík |
| collection | DOAJ |
| description | The first boundary-value problem for an autonomous second-order system of linear partial differential equations of parabolic type with a single delay is considered. Assuming that a decomposition of the given system into a system of independent scalar second-order linear partial differential equations of parabolic type with a single delay is possible, an analytical
solution to the problem is given in the form of formal series and the character of their convergence is discussed. A delayed exponential function is used in order to analytically solve auxiliary initial problems (arising when Fourier method is applied) for ordinary linear differential equations of the first order with a single delay. |
| format | Article |
| id | doaj-art-df4ad3fe3d0242939f36615b21b651d2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-df4ad3fe3d0242939f36615b21b651d22025-02-03T01:33:27ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/219040219040Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single DelayJosef Diblík0Denis Khusainov1Oleksandra Kukharenko2Zdeněk Svoboda3Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, 60200 Brno, Czech RepublicDepartment of Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv 01601, UkraineDepartment of Cybernetics, Taras Shevchenko National University of Kyiv, Kyiv 01601, UkraineDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicThe first boundary-value problem for an autonomous second-order system of linear partial differential equations of parabolic type with a single delay is considered. Assuming that a decomposition of the given system into a system of independent scalar second-order linear partial differential equations of parabolic type with a single delay is possible, an analytical solution to the problem is given in the form of formal series and the character of their convergence is discussed. A delayed exponential function is used in order to analytically solve auxiliary initial problems (arising when Fourier method is applied) for ordinary linear differential equations of the first order with a single delay.http://dx.doi.org/10.1155/2012/219040 |
| spellingShingle | Josef Diblík Denis Khusainov Oleksandra Kukharenko Zdeněk Svoboda Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay Abstract and Applied Analysis |
| title | Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay |
| title_full | Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay |
| title_fullStr | Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay |
| title_full_unstemmed | Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay |
| title_short | Solution of the First Boundary-Value Problem for a System of Autonomous Second-Order Linear Partial Differential Equations of Parabolic Type with a Single Delay |
| title_sort | solution of the first boundary value problem for a system of autonomous second order linear partial differential equations of parabolic type with a single delay |
| url | http://dx.doi.org/10.1155/2012/219040 |
| work_keys_str_mv | AT josefdiblik solutionofthefirstboundaryvalueproblemforasystemofautonomoussecondorderlinearpartialdifferentialequationsofparabolictypewithasingledelay AT deniskhusainov solutionofthefirstboundaryvalueproblemforasystemofautonomoussecondorderlinearpartialdifferentialequationsofparabolictypewithasingledelay AT oleksandrakukharenko solutionofthefirstboundaryvalueproblemforasystemofautonomoussecondorderlinearpartialdifferentialequationsofparabolictypewithasingledelay AT zdeneksvoboda solutionofthefirstboundaryvalueproblemforasystemofautonomoussecondorderlinearpartialdifferentialequationsofparabolictypewithasingledelay |