Large-time asymptotic equivalence for a class of non-autonomous semilinear parabolic equations
It is proved a result concerning the long-time behavior of solutions to a class of non-autonomous semilinear parabolic Neumann boundary-value problems defined on an open bounded connected subset \(\Omega\) of \(\mathbb{R}^N\). The nature of the equations that are investigated leads to considering of two complementary situations, according to whether the time-dependent lower order terms in the equations possess recurrence properties. The method of proof rests upon the use of comparison principles and upon the existence of exponential dichotomies for the family of evolution operators associated with the principal part of the equations.
scientific article; zbMATH DE number 1197146
scientific article