Exponential stability, change of stability and eigenvalue problems for linear time-periodic parabolic equations on $$\mathbb R^N$$

Preprint (PDF) 1993
Differential and Integral Equations 7 (1994), 1265-1284
The main purpose of this article is to give conditions on a nonnegative weight function $$m$$ which are necessary and sufficient for the zero solution of the linear time-periodic parabolic equation $\partial_t u-\Delta u=-m(x,t)u \quad\text{in }\mathbb R^N\times(0,\infty)$ to be exponentially stable and to apply these results to the study of change of stability in parameter dependent time-periodic parabolic problems.