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

Daniel Daners and Pablo Koch Medina
Preprint (PDF) 1993
Differential and Integral Equations 7 (1994), 1265-1284
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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.

A preprint (PDF) is available.

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