2011/10/05 by Nicholas D. Brubaker, Brubaker, Nicholas D., Alan E. Lindsay +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1110.0890
32 pages, 11 figures, change in formatting
arxiv created 2011/11/01 · arxiv updated 2011/11/02
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.