Study On A Class Of Non-local Hyperbolic Problems Involving MEMS Model Equations

In this paper,we study the following non-local hyperbolic problem:where ?,?,p are non-negative constants and F has a singularity at 1.We prove the equation has a local solution if the initial value is small enough,and has a global solution when there exists a critical mass ?0 and ?>?0 in chapter 2.After a brief discussion about the steady state of equation in chapter 3,we prove that the equation has different quenching conditions depending on ?,?,p,? and F in chapter 4.Finally in chapter 5 we prove the main results by numerical solution.The content of this paper is a extension of[N.I.Kavallaris,A.A.Lacey,C.V.Nikolopoulos and D.E.Tzanetis.A hyperbolic non-local problem modelling MEMS technology.Rocky Mountain J.Math.41(2)2011 505-534],and the results we obtained can be applied to many similar MEMS equations.