On the solvability of a variational inequality problem and application to a problem of two membranes
The purpose of this work is to give a continuous convex function, for which we can characterize the subdifferential, in order to reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, w...
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Hindawi Limited
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004823 |
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doaj-cdd4c307419b4a75943f04d4a4911a532020-11-25T00:19:11ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0125960360810.1155/S0161171201004823On the solvability of a variational inequality problem and application to a problem of two membranesA. Addou0E. B. Mermri1University Mohamed I, Faculty of Sciences, Department of Mathematics and Computer Sciences, Oujda, MoroccoUniversity Mohamed I, Faculty of Sciences, Department of Mathematics and Computer Sciences, Oujda, MoroccoThe purpose of this work is to give a continuous convex function, for which we can characterize the subdifferential, in order to reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, where f belongs to L2(Ω)×L2(Ω) and K={v∈H01(Ω)×H01(Ω):v1≥v2 a.e. in Ω}.http://dx.doi.org/10.1155/S0161171201004823 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. Addou E. B. Mermri |
| spellingShingle |
A. Addou E. B. Mermri On the solvability of a variational inequality problem and application to a problem of two membranes International Journal of Mathematics and Mathematical Sciences |
| author_facet |
A. Addou E. B. Mermri |
| author_sort |
A. Addou |
| title |
On the solvability of a variational inequality problem and application to a problem of two membranes |
| title_short |
On the solvability of a variational inequality problem and application to a problem of two membranes |
| title_full |
On the solvability of a variational inequality problem and application to a problem of two membranes |
| title_fullStr |
On the solvability of a variational inequality problem and application to a problem of two membranes |
| title_full_unstemmed |
On the solvability of a variational inequality problem and application to a problem of two membranes |
| title_sort |
on the solvability of a variational inequality problem and application to a problem of two membranes |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2001-01-01 |
| description |
The purpose of this work is to give a continuous convex function,
for which we can characterize the subdifferential, in order to
reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, where f belongs to L2(Ω)×L2(Ω) and K={v∈H01(Ω)×H01(Ω):v1≥v2 a.e. in Ω}. |
| url |
http://dx.doi.org/10.1155/S0161171201004823 |
| work_keys_str_mv |
AT aaddou onthesolvabilityofavariationalinequalityproblemandapplicationtoaproblemoftwomembranes AT ebmermri onthesolvabilityofavariationalinequalityproblemandapplicationtoaproblemoftwomembranes |
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1725372809267380224 |