Abstract
In this work we study the semilinear wave equation of the form
utt = uxx + lambda/(1 − u)2;
with homogeneous Dirichlet boundary conditions and suitable initial conditions, which, under appropriate circumstances, serves as a model of an idealized electrostatically actuated MEMS device. First we establish local existence of the solutions of the problem for any lambda > 0: Then we focus on the singular behaviour of the solution, which occurs through
finitetime quenching, i.e. when u(·; t)1 → 1 as t →t*− < ∞, investigating both conditions for quenching and the quenching profile of u: To this end, the nonexistence of a regular similarity solution near a quenching point is first shown and then a formal asymptotic expansion is used to determine the local form of the solution. Finally, using a finite difference scheme, we solve the problem numerically, illustrating the preceding results.
utt = uxx + lambda/(1 − u)2;
with homogeneous Dirichlet boundary conditions and suitable initial conditions, which, under appropriate circumstances, serves as a model of an idealized electrostatically actuated MEMS device. First we establish local existence of the solutions of the problem for any lambda > 0: Then we focus on the singular behaviour of the solution, which occurs through
finitetime quenching, i.e. when u(·; t)1 → 1 as t →t*− < ∞, investigating both conditions for quenching and the quenching profile of u: To this end, the nonexistence of a regular similarity solution near a quenching point is first shown and then a formal asymptotic expansion is used to determine the local form of the solution. Finally, using a finite difference scheme, we solve the problem numerically, illustrating the preceding results.
Original language  English 

Article number  13 
Pages (fromto)  10091037 
Number of pages  29 
Journal  Discrete and Continuous Dynamical SystemsSeries A 
Volume  35 
Issue number  3 
Early online date  1 Oct 2014 
DOIs  
Publication status  Published  Mar 2015 
Keywords
 Electrostatic MEMS
 Quenching of Solution
 Hyperbolic Problems
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Profiles

Andrew Alfred Lacey
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)