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

Abstract

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.