Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators
The nonlocal boundary value problem for the parabolic differential equation v'(t)+A(t)v(t)=f(t) (0≤t≤T), v(0)=v(λ)+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/519814 |
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| author | Allaberen Ashyralyev Asker Hanalyev |
| author_facet | Allaberen Ashyralyev Asker Hanalyev |
| author_sort | Allaberen Ashyralyev |
| collection | DOAJ |
| description | The nonlocal boundary value problem for the parabolic differential equation v'(t)+A(t)v(t)=f(t) (0≤t≤T), v(0)=v(λ)+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β) of all Eα-β-valued continuous functions φ(t) on [0,T] satisfying a Hölder condition with a weight (t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established. |
| format | Article |
| id | doaj-art-01bd90d23f844f4b9f7d6c87a97582fc |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-01bd90d23f844f4b9f7d6c87a97582fc2025-08-20T02:01:49ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/519814519814Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent OperatorsAllaberen Ashyralyev0Asker Hanalyev1Department of Mathematics, Fatih University, 34500 Istanbul, TurkeyTejen High School, Tejen, TurkmenistanThe nonlocal boundary value problem for the parabolic differential equation v'(t)+A(t)v(t)=f(t) (0≤t≤T), v(0)=v(λ)+φ, 0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β) of all Eα-β-valued continuous functions φ(t) on [0,T] satisfying a Hölder condition with a weight (t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.http://dx.doi.org/10.1155/2014/519814 |
| spellingShingle | Allaberen Ashyralyev Asker Hanalyev Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators The Scientific World Journal |
| title | Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators |
| title_full | Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators |
| title_fullStr | Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators |
| title_full_unstemmed | Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators |
| title_short | Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators |
| title_sort | well posedness of nonlocal parabolic differential problems with dependent operators |
| url | http://dx.doi.org/10.1155/2014/519814 |
| work_keys_str_mv | AT allaberenashyralyev wellposednessofnonlocalparabolicdifferentialproblemswithdependentoperators AT askerhanalyev wellposednessofnonlocalparabolicdifferentialproblemswithdependentoperators |