On the Asymptotic Behavior of Solutions of Nonlinear Second-Order Parabolic Equations

We study the asymptotic behavior as $t\to+\infty$ of solutions to a semilinear second-order parabolic equation in a cylindrical domain bounded in the spatial variable. We find the leading term of the asymptotic expansion of a solution as $t\to+\infty$ and show that each solution of the problem under consideration is asymptotically equivalent to a solution of some nonlinear ordinary differential equation.