Geodesic
An Elastic Membrane With an Attached Non-Linear Thermoelastic Rod
International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) no. 4, pp. 479-486

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We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain W is subset R2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence of a unique global weak solution to this problem using a fixed point argument.
Keywords: thermoelastic materials, non-linear partial differential equations
Mots-clés : materiałoznawstwo 
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     author = {Horn, W. and Soko{\l}owski, J.},
     title = {An {Elastic} {Membrane} {With} an {Attached} {Non-Linear} {Thermoelastic} {Rod}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {479--486},
     publisher = {mathdoc},
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     number = {4},
     year = {2002},
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     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_4_a1/}
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Horn, W.; Sokołowski, J. An Elastic Membrane With an Attached Non-Linear Thermoelastic Rod. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) no. 4, pp. 479-486. http://geodesic.mathdoc.fr/item/IJAMCS_2002_12_4_a1/