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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/24ab373b3951cb18a5f9702118a34d49d/elkepeter",         
         "tags" : [
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         "intraHash" : "4ab373b3951cb18a5f9702118a34d49d",
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         "label" : "A free boundary value problem modelling microelectromechanical systems with general permittivity",
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         "journal": "Nonlinear Anal. Real World Appl.",
         "year": "2015", 
         "url": "https://doi.org/10.1016/j.nonrwa.2015.03.008", 
         
         "author": [ 
            "Christina Lienstromberg"
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         "authors": [
         	
            	{"first" : "Christina",	"last" : "Lienstromberg"}
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         "volume": "25","pages": "190--218","abstract": "\"An investigation of the free boundary value problem arising from the modelling of electrostatically actuated microelectromechanical systems with general permittivity is presented. Consisting of a parabolic evolution problem for the displacement of a membrane as well as of an elliptic moving boundary problem for the electric potential between the membrane and a rigid ground plate, the system is shown to be well-posed locally in time for all values λ of the applied voltage. It is in addition verified that the solution exists even globally in time, provided that the applied voltage does not exceed a certain critical value λ∗. Furthermore, we establish the convergence of the solution of the free boundary problem towards the solution of the small-aspect ratio model, as the aspect ratio tends to zero.''",
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         "fjournal" : "Nonlinear Analysis. Real World Applications. An International\r\n              Multidisciplinary Journal",
         
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         "label" : "A qualitative analysis of solutions to microelectromechanical systems with curvature and nonlinear permittivity profile",
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         "journal": "Comm. Partial Differential Equations",
         "year": "2016", 
         "url": "https://doi.org/10.1080/03605302.2015.1105259", 
         
         "author": [ 
            "Joachim Escher","Christina Lienstromberg"
         ],
         "authors": [
         	
            	{"first" : "Joachim",	"last" : "Escher"},
            	{"first" : "Christina",	"last" : "Lienstromberg"}
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         "mrreviewer" : "Corentin Audiard",
         
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         "label" : "On qualitative properties of solutions to microelectromechanical systems with general permittivity",
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         "author": [ 
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         "volume": "179","number": "4","pages": "581--602","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.''",
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         "fjournal" : "Monatshefte für Mathematik",
         
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         "year": "2016", 
         "url": "https://doi.org/10.1007/s10231-016-0549-8", 
         
         "author": [ 
            "Joachim Escher","Christina Lienstromberg"
         ],
         "authors": [
         	
            	{"first" : "Joachim",	"last" : "Escher"},
            	{"first" : "Christina",	"last" : "Lienstromberg"}
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         "journal": "Nonlinearity",
         "year": "2017", 
         "url": "https://doi.org/10.1088/1361-6544/aa4ff9", 
         
         "author": [ 
            "Joachim Escher","Pierre Gosselet","Christina Lienstromberg"
         ],
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            	{"first" : "Joachim",	"last" : "Escher"},
            	{"first" : "Pierre",	"last" : "Gosselet"},
            	{"first" : "Christina",	"last" : "Lienstromberg"}
         ],
         "volume": "30","number": "2","pages": "454--465","abstract": "\"Numerical evidence is provided that there are non-constant permittivity profiles which force solutions to a two-dimensional coupled moving boundary problem modelling microelectromechanical systems to be positive, while the corresponding small-aspect ratio model produces solutions which are always non-positive.''",
         "mrclass" : "35R35 (35B09 35B44 35K20 35K58 74M05)",
         
         "fjournal" : "Nonlinearity",
         
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