Differential difference inequalities related to parabolic functional differential equations
Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions fo...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2010-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol30/1/art/opuscula_math_3007.pdf |
| _version_ | 1828485258147790848 |
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| author | Milena Netka |
| author_facet | Milena Netka |
| author_sort | Milena Netka |
| collection | DOAJ |
| description | Initial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the method of lines is given. Nonlinear estimates of the Perron type for given operators with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables. |
| first_indexed | 2024-12-11T09:09:50Z |
| format | Article |
| id | doaj.art-2591524021824a93861230e2cc60f9db |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-11T09:09:50Z |
| publishDate | 2010-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-2591524021824a93861230e2cc60f9db2022-12-22T01:13:31ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742010-01-0130195115http://dx.doi.org/10.7494/OpMath.2010.30.1.953007Differential difference inequalities related to parabolic functional differential equationsMilena Netka0University of Gdańsk, Institute of Mathematics, ul. Wita Stwosza 57, 80-952 Gdańsk, PolandInitial boundary value problems for nonlinear parabolic functional differential equations are transformed by discretization in space variables into systems of ordinary functional differential equations. A comparison theorem for differential difference inequalities is proved. Sufficient conditions for the convergence of the method of lines is given. Nonlinear estimates of the Perron type for given operators with respect to functional variables are used. Results obtained in the paper can be applied to differential integral problems and to equations with deviated variables.http://www.opuscula.agh.edu.pl/vol30/1/art/opuscula_math_3007.pdfparabolic functional differential equationsmethod of linesstability and convergence |
| spellingShingle | Milena Netka Differential difference inequalities related to parabolic functional differential equations Opuscula Mathematica parabolic functional differential equations method of lines stability and convergence |
| title | Differential difference inequalities related to parabolic functional differential equations |
| title_full | Differential difference inequalities related to parabolic functional differential equations |
| title_fullStr | Differential difference inequalities related to parabolic functional differential equations |
| title_full_unstemmed | Differential difference inequalities related to parabolic functional differential equations |
| title_short | Differential difference inequalities related to parabolic functional differential equations |
| title_sort | differential difference inequalities related to parabolic functional differential equations |
| topic | parabolic functional differential equations method of lines stability and convergence |
| url | http://www.opuscula.agh.edu.pl/vol30/1/art/opuscula_math_3007.pdf |
| work_keys_str_mv | AT milenanetka differentialdifferenceinequalitiesrelatedtoparabolicfunctionaldifferentialequations |