Periodic solutions for a class of nonlinear parabolic equations

Abstract

In this article, we prove that nonlinear parabolic equation

has a solution u(t, x) which is ω-periodic with respect to the time variable t. The period ω > 0 is arbitrarily chosen and fixed. We propose a new approach to investigate the periodicity problem of this equation. This approach gives new results.

Keywords:

• nonlinear parabolic equations
• periodic solutions
• existence

AMS Subject Classifications::

• 35K55
• 35B10

Acknowledgements

This article is supported by the grant DD-VU 02/90, Bulgaria.