Well-posedness and asymptotic behavior of solutions to a second order nonlocal parabolic MEMS equation

Yufei Wei, Yanyan Zhang

We consider a second-order nonlocal parabolic MEMS equation with Dirichlet boundary conditions: \[ u_t-Δu=\fracλ{(1-u)^2\bigl(1+\int_Ω\frac{1}{1-u}\,dx\bigr)^2},\quad x\inΩ,\ t…