Analysis of the singular solution branch of a prescribed mean curvature equation with singular nonlinearity

Autor:	Brubaker, Nicholas D., Lindsay, Alan E.
Rok vydání:	2011
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	The existence and multiplicity of solutions to a quasilinear, elliptic partial differential equation (PDE) with singular non-linearity is analyzed. The PDE is a recently derived variant of a canonical model used in the modeling of Micro-Electro Mechanical Systems (MEMS). It is observed that the bifurcation curve of solutions terminates at single dead-end point, beyond which no classical solutions exist. A necessary condition for the existence of solutions is developed which reveals that this dead-end point corresponds to a blow-up in the solution derivative at a point internal to the domain. Using asymptotic analysis, an accurate prediction of this dead end point is obtained. An arc-length parameterization of the solution curve can be employed to continue solutions beyond the dead end point, however, all extra solutions are found to be multi-valued. Comment: 32 pages, 11 figures, change in formatting
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1110.0890 Zobrazit plný text záznamu View this record from Arxiv