Asymptotic behavior of solutions to nonlinear parabolic equations with nonlocal terms. (English) Zbl 1089.35027
Summary: The asymptotic behavior of the solutions, as time goes to infinity, to nonlinear parabolic equations with two classes of nonlocal terms is investigated. One of the important features of our problems is that equilibria may be a continuum which is diffeomorphic to a piece of curve in \(\mathbb{R}^2\).
MSC:
35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
35K55 | Nonlinear parabolic equations |
35B40 | Asymptotic behavior of solutions to PDEs |
45K05 | Integro-partial differential equations |