A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations
The abstract nonlocal boundary value problem \begin{equation*}\left\{\begin{array}{l} -\frac{d^{2}u(t)}{dt^{2}}+sign(t)Au(t)=g(t),(0\leq t\leq 1), \\ \frac{du(t)}{dt}+sign(t)Au(t)=f(t),(-1\leq t\leq 0), \\ u(1)=u(-1)+\mu \end{array}\right.\end{equation*} for the differential equation in a Hilbert sp...
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| Format: | Article |
| Language: | English |
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University of Szeged
2011-07-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=798 |
| _version_ | 1797830738774589440 |
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| author | A. Ashyralyev |
| author_facet | A. Ashyralyev |
| author_sort | A. Ashyralyev |
| collection | DOAJ |
| description | The abstract nonlocal boundary value problem
\begin{equation*}\left\{\begin{array}{l}
-\frac{d^{2}u(t)}{dt^{2}}+sign(t)Au(t)=g(t),(0\leq t\leq 1), \\
\frac{du(t)}{dt}+sign(t)Au(t)=f(t),(-1\leq t\leq 0), \\
u(1)=u(-1)+\mu
\end{array}\right.\end{equation*}
for the differential equation in a Hilbert space $H$ with the self-adjoint positive definite operator $A$ is considered. The well-posedness of this problem in Hölder spaces without a weight is established. The coercivity inequalities for solutions of the boundary value problem for elliptic-parabolic equations are obtained. |
| first_indexed | 2024-04-09T13:40:54Z |
| format | Article |
| id | doaj.art-c619db98d198479cb75be193bf02c065 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:54Z |
| publishDate | 2011-07-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-c619db98d198479cb75be193bf02c0652023-05-09T07:53:01ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752011-07-0120114911610.14232/ejqtde.2011.1.49798A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equationsA. Ashyralyev0Fatih University, Istanbul, TurkeyThe abstract nonlocal boundary value problem \begin{equation*}\left\{\begin{array}{l} -\frac{d^{2}u(t)}{dt^{2}}+sign(t)Au(t)=g(t),(0\leq t\leq 1), \\ \frac{du(t)}{dt}+sign(t)Au(t)=f(t),(-1\leq t\leq 0), \\ u(1)=u(-1)+\mu \end{array}\right.\end{equation*} for the differential equation in a Hilbert space $H$ with the self-adjoint positive definite operator $A$ is considered. The well-posedness of this problem in Hölder spaces without a weight is established. The coercivity inequalities for solutions of the boundary value problem for elliptic-parabolic equations are obtained.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=798elliptic-parabolic equationnonlocal boundary-value problemwell-posedness |
| spellingShingle | A. Ashyralyev A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations Electronic Journal of Qualitative Theory of Differential Equations elliptic-parabolic equation nonlocal boundary-value problem well-posedness |
| title | A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations |
| title_full | A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations |
| title_fullStr | A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations |
| title_full_unstemmed | A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations |
| title_short | A note on the well-posedness of the nonlocal boundary value problem for elliptic-parabolic equations |
| title_sort | note on the well posedness of the nonlocal boundary value problem for elliptic parabolic equations |
| topic | elliptic-parabolic equation nonlocal boundary-value problem well-posedness |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=798 |
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