Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces
A first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem −𝑑2𝑢(𝑡)/𝑑𝑡2+sign(𝑡)𝐴𝑢(𝑡)=𝑔(𝑡), (0≤𝑡≤1), 𝑑𝑢(𝑡)/𝑑𝑡+sign(𝑡)𝐴𝑢(𝑡)=𝑓(𝑡), (−1≤𝑡≤0), 𝑢(0+)=𝑢(0−),𝑢(0+)=𝑢(0−),and𝑢(1)=𝑢(−1)+𝜇 for differential equations in a Hilbert space 𝐻 with a self-adj...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/237657 |
| _version_ | 1798045927945011200 |
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| author | Okan Gercek |
| author_facet | Okan Gercek |
| author_sort | Okan Gercek |
| collection | DOAJ |
| description | A first order of accuracy difference scheme for the
approximate solution of abstract nonlocal boundary value problem −𝑑2𝑢(𝑡)/𝑑𝑡2+sign(𝑡)𝐴𝑢(𝑡)=𝑔(𝑡), (0≤𝑡≤1), 𝑑𝑢(𝑡)/𝑑𝑡+sign(𝑡)𝐴𝑢(𝑡)=𝑓(𝑡), (−1≤𝑡≤0), 𝑢(0+)=𝑢(0−),𝑢(0+)=𝑢(0−),and𝑢(1)=𝑢(−1)+𝜇 for differential equations in a Hilbert space 𝐻 with a self-adjoint positive definite operator A is considered. The well-posedness of this difference scheme in Hölder spaces without a weight is established. Moreover, as applications, coercivity estimates in Hölder norms
for the solutions of nonlocal boundary value problems for elliptic-parabolic equations are obtained. |
| first_indexed | 2024-04-11T23:29:08Z |
| format | Article |
| id | doaj.art-88fc332ad38f43128af6bd302f2acb2e |
| institution | Directory Open Access Journal |
| issn | 1085-3375 1687-0409 |
| language | English |
| last_indexed | 2024-04-11T23:29:08Z |
| publishDate | 2012-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj.art-88fc332ad38f43128af6bd302f2acb2e2022-12-22T03:57:14ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/237657237657Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder SpacesOkan Gercek0Department of Mathematics, Fatih University, 34500 Buyukcekmece, Istanbul, TurkeyA first order of accuracy difference scheme for the approximate solution of abstract nonlocal boundary value problem −𝑑2𝑢(𝑡)/𝑑𝑡2+sign(𝑡)𝐴𝑢(𝑡)=𝑔(𝑡), (0≤𝑡≤1), 𝑑𝑢(𝑡)/𝑑𝑡+sign(𝑡)𝐴𝑢(𝑡)=𝑓(𝑡), (−1≤𝑡≤0), 𝑢(0+)=𝑢(0−),𝑢(0+)=𝑢(0−),and𝑢(1)=𝑢(−1)+𝜇 for differential equations in a Hilbert space 𝐻 with a self-adjoint positive definite operator A is considered. The well-posedness of this difference scheme in Hölder spaces without a weight is established. Moreover, as applications, coercivity estimates in Hölder norms for the solutions of nonlocal boundary value problems for elliptic-parabolic equations are obtained.http://dx.doi.org/10.1155/2012/237657 |
| spellingShingle | Okan Gercek Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces Abstract and Applied Analysis |
| title | Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces |
| title_full | Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces |
| title_fullStr | Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces |
| title_full_unstemmed | Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces |
| title_short | Well-Posedness of the First Order of Accuracy Difference Scheme for Elliptic-Parabolic Equations in Hölder Spaces |
| title_sort | well posedness of the first order of accuracy difference scheme for elliptic parabolic equations in holder spaces |
| url | http://dx.doi.org/10.1155/2012/237657 |
| work_keys_str_mv | AT okangercek wellposednessofthefirstorderofaccuracydifferenceschemeforellipticparabolicequationsinholderspaces |