%0 Journal Article %1 MR3474882 %A Lienstromberg, Christina %D 2016 %J Monatsh. Math. %K IADM microelectromechanical solutions Lienstromberg systems qualitative from:elkepeter of to properties %N 4 %P 581--602 %R 10.1007/s00605-015-0744-5 %T On qualitative properties of solutions to microelectromechanical systems with general permittivity %U https://doi.org/10.1007/s00605-015-0744-5 %V 179 %X "Qualitative properties of solutions to the evolution problem modelling microelectromechanical systems with general permittivity profile are investigated. The system couples a parabolic evolution problem for the displacement of a membrane with an elliptic free boundary value problem for the electric potential in the region between the membrane and a rigid ground plate. We briefly allude to results concerning local and global well-posedness and the small-apect ratio limit. However, the focus is here on proving non-positivity of the membrane displacement for the full moving boundary problem under certain boundary conditions on the potential, as well as the existence of finite-time singularities assuming to have a non-positive solution.''

@article{MR3474882, abstract = {"Qualitative properties of solutions to the evolution problem modelling microelectromechanical systems with general permittivity profile are investigated. The system couples a parabolic evolution problem for the displacement of a membrane with an elliptic free boundary value problem for the electric potential in the region between the membrane and a rigid ground plate. We briefly allude to results concerning local and global well-posedness and the small-apect ratio limit. However, the focus is here on proving non-positivity of the membrane displacement for the full moving boundary problem under certain boundary conditions on the potential, as well as the existence of finite-time singularities assuming to have a non-positive solution.''}, added-at = {2023-03-27T11:14:19.000+0200}, author = {Lienstromberg, Christina}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2529e2a96561412f7c16f2c7875622058/mathematik}, doi = {10.1007/s00605-015-0744-5}, fjournal = {Monatshefte f\"{u}r Mathematik}, interhash = {462824bdb76c7d72e72898a1d2d0dc02}, intrahash = {529e2a96561412f7c16f2c7875622058}, issn = {0026-9255}, journal = {Monatsh. Math.}, keywords = {IADM microelectromechanical solutions Lienstromberg systems qualitative from:elkepeter of to properties}, mrclass = {35R35 (35B09 35B44 35Q74 74M05)}, mrnumber = {3474882}, number = 4, pages = {581--602}, timestamp = {2023-12-05T17:17:37.000+0100}, title = {On qualitative properties of solutions to microelectromechanical systems with general permittivity}, url = {https://doi.org/10.1007/s00605-015-0744-5}, volume = 179, year = 2016 }