NUMERICAL CRITICAL VALUE OF THE GENERALIZED PARABOLIC MEMS EQUATION

In this paper, we study the semidiscrete approximation for the following initial-boundary value problem -v(t)(x,t) = -Dv(xx)(x,t) + lambda f(x)(L + v(x,t))(-P), -l < x < l, t > 0, v(-l, t) = 0, v(l, t) = 0, t > 0, v(x, 0) = v(0)(x) = 0, -l <= x <= l, where D > 0, lambda > 0, p > 1 and f(x) is an element of C-1([-l, l]), symmetric and nondecreasing on the interval (-l, 0), 0 < f(x) < 1, f(-l) = 0, f(l) = 0 and 1 = 1/2. We determine the critical value of a semidiscrete form of above problem. We also show that the semidiscrete quenching time in certain cases converges to the real one when the mesh size tends to zero. Finally, we give some numerical experiments to illustrate our analysis.