Estimates for the principal spectrum point for certain time-dependent parabolic operators (Q2706580)

Nonauthonomous linear parabolic equations with time-periodic and almost periodic coefficients are considered. In the time-periodic case, the authors establish bounds for principal eigenvalues. Besides they reduce the periodic problem for parabolic equations to an elliptic operator. The main tool here is the time-averaging. It is then shown that an analogous bound can be derived for principal points of the spectrum of nonauthonomous parabolic equations with almost periodic coefficients. These results have applications to the stability of nonlinear parabolic equations.