On well-posedness of the nonlocal boundary value problem for parabolic difference equations
We consider the nonlocal boundary value problem for difference equations (uk−uk−1)/τ+Auk=φk, 1≤k≤N, Nτ=1, and u0=u[λ/τ]+φ, 0<λ≤1, in an arbitrary Banach space E with the strongly positive operator A. The well-posedness of this nonlocal boundary value problem for difference equations in various...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/S1026022604403033 |
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| author | A. Ashyralyev I. Karatay P. E. Sobolevskii |
| author_facet | A. Ashyralyev I. Karatay P. E. Sobolevskii |
| author_sort | A. Ashyralyev |
| collection | DOAJ |
| description | We consider the nonlocal boundary value problem for difference
equations (uk−uk−1)/τ+Auk=φk, 1≤k≤N, Nτ=1, and u0=u[λ/τ]+φ, 0<λ≤1, in an
arbitrary Banach space E with the strongly positive operator
A. The well-posedness of this nonlocal boundary value problem
for difference equations in various Banach spaces is studied. In
applications, the stability and coercive stability estimates in
Hölder norms for the solutions of the difference
scheme of the mixed-type boundary value problems for the
parabolic equations are obtained. Some results of numerical
experiments are given. |
| format | Article |
| id | doaj-art-edba1d0ce84947a6b47e5a8b73e7ca5e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-edba1d0ce84947a6b47e5a8b73e7ca5e2025-02-03T05:52:54ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2004-01-012004227328610.1155/S1026022604403033On well-posedness of the nonlocal boundary value problem for parabolic difference equationsA. Ashyralyev0I. Karatay1P. E. Sobolevskii2Department of Mathematics, Fatih University, 34900 Büyükçekmece, Istanbul, TurkeyDepartment of Mathematics, Fatih University, 34900 Büyükçekmece, Istanbul, TurkeyInstitute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, IsraelWe consider the nonlocal boundary value problem for difference equations (uk−uk−1)/τ+Auk=φk, 1≤k≤N, Nτ=1, and u0=u[λ/τ]+φ, 0<λ≤1, in an arbitrary Banach space E with the strongly positive operator A. The well-posedness of this nonlocal boundary value problem for difference equations in various Banach spaces is studied. In applications, the stability and coercive stability estimates in Hölder norms for the solutions of the difference scheme of the mixed-type boundary value problems for the parabolic equations are obtained. Some results of numerical experiments are given.http://dx.doi.org/10.1155/S1026022604403033 |
| spellingShingle | A. Ashyralyev I. Karatay P. E. Sobolevskii On well-posedness of the nonlocal boundary value problem for parabolic difference equations Discrete Dynamics in Nature and Society |
| title | On well-posedness of the nonlocal boundary value problem for parabolic difference equations |
| title_full | On well-posedness of the nonlocal boundary value problem for parabolic difference equations |
| title_fullStr | On well-posedness of the nonlocal boundary value problem for parabolic difference equations |
| title_full_unstemmed | On well-posedness of the nonlocal boundary value problem for parabolic difference equations |
| title_short | On well-posedness of the nonlocal boundary value problem for parabolic difference equations |
| title_sort | on well posedness of the nonlocal boundary value problem for parabolic difference equations |
| url | http://dx.doi.org/10.1155/S1026022604403033 |
| work_keys_str_mv | AT aashyralyev onwellposednessofthenonlocalboundaryvalueproblemforparabolicdifferenceequations AT ikaratay onwellposednessofthenonlocalboundaryvalueproblemforparabolicdifferenceequations AT pesobolevskii onwellposednessofthenonlocalboundaryvalueproblemforparabolicdifferenceequations |