Exact controllability of a second order integro-differential equation with a pressure term
This paper is concerned with the boundary exact controllability of the equation $$u''-\Delta u-\int_0^t g(t-\sigma)\Delta u(\sigma) d\sigma=-\nabla p$$ where $Q$ is a finite cilinder $\Omega\times]0,T[$, $\Omega$ is a bounded domain of $R^n$, $u=(u_1(x,t),\ldots,u_n(x,t))$, $x=(x_1,\ldots,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
1998-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=14 |
| _version_ | 1797830809905790976 |
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| author | Marcelo Cavalcanti V. N. D. Cavalcanti A. Rocha J. A. Soriano |
| author_facet | Marcelo Cavalcanti V. N. D. Cavalcanti A. Rocha J. A. Soriano |
| author_sort | Marcelo Cavalcanti |
| collection | DOAJ |
| description | This paper is concerned with the boundary exact controllability of the equation $$u''-\Delta u-\int_0^t g(t-\sigma)\Delta u(\sigma) d\sigma=-\nabla p$$ where $Q$ is a finite cilinder $\Omega\times]0,T[$, $\Omega$ is a bounded domain of $R^n$, $u=(u_1(x,t),\ldots,u_n(x,t))$, $x=(x_1,\ldots,x_n)$ are $n$-dimensional vectors and $p$ denotes the pressure term. The result is obtained by applying HUM (Hilbert Uniqueness Method) due to J. L. Lions. The above equation is a simple model of dynamical elasticity equations for incompressible materials with memory. |
| first_indexed | 2024-04-09T13:42:01Z |
| format | Article |
| id | doaj.art-d9a33aca32a24569a758ce0cb7dd42fd |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:42:01Z |
| publishDate | 1998-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-d9a33aca32a24569a758ce0cb7dd42fd2023-05-09T07:52:56ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38751998-01-011998911810.14232/ejqtde.1998.1.914Exact controllability of a second order integro-differential equation with a pressure termMarcelo Cavalcanti0V. N. D. Cavalcanti1A. Rocha2J. A. Soriano3Universidade Estadual de Maringá, BrasilUniversidade Estadual de Maringá, BrasilUniversidade Federal do Rio de Janeiro, BrasilUniversidade Estadual de Maringá, BrasilThis paper is concerned with the boundary exact controllability of the equation $$u''-\Delta u-\int_0^t g(t-\sigma)\Delta u(\sigma) d\sigma=-\nabla p$$ where $Q$ is a finite cilinder $\Omega\times]0,T[$, $\Omega$ is a bounded domain of $R^n$, $u=(u_1(x,t),\ldots,u_n(x,t))$, $x=(x_1,\ldots,x_n)$ are $n$-dimensional vectors and $p$ denotes the pressure term. The result is obtained by applying HUM (Hilbert Uniqueness Method) due to J. L. Lions. The above equation is a simple model of dynamical elasticity equations for incompressible materials with memory.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=14 |
| spellingShingle | Marcelo Cavalcanti V. N. D. Cavalcanti A. Rocha J. A. Soriano Exact controllability of a second order integro-differential equation with a pressure term Electronic Journal of Qualitative Theory of Differential Equations |
| title | Exact controllability of a second order integro-differential equation with a pressure term |
| title_full | Exact controllability of a second order integro-differential equation with a pressure term |
| title_fullStr | Exact controllability of a second order integro-differential equation with a pressure term |
| title_full_unstemmed | Exact controllability of a second order integro-differential equation with a pressure term |
| title_short | Exact controllability of a second order integro-differential equation with a pressure term |
| title_sort | exact controllability of a second order integro differential equation with a pressure term |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=14 |
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