On the existence and pointwise stability of periodic solutions to a linear parabolic equation in unbounded domains

Abstract

It is proved that a linear parabolic partial differential equation in an unbounded domain admits a unique time periodic solution, provided the data are time-periodic. Moreover, pointwise stability of solutions are established via a suitable maximum principle.

Keywords:

• Parabolic equations
• unbounded domains

AMS:

• 35K15
• 35K50