Periodic solutions for a class of nonlinear parabolic equations. (English) Zbl 1271.35049
Summary: In this article, we prove that nonlinear parabolic equation
\[
u_t-\Delta u=f(t,x,u,u_x)
\]
has a solution \(u(t,x)\) which is \(\omega\)-periodic with respect to the time variable \(t\). The period \(\omega>0\) is arbitrarily chosen and fixed. We propose a new approach to investigate the periodicity problem of this equation. This approach gives new results.
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