Blow-Up and Convergence Results for a One-Dimensional Non-Local Parabolic Problem

Abstract

Considering a one-dimensional non-local semilinear parabolic problem, it is shown that blow-up in finite time occurs for suitable large initial conditions. The asymptotic behavior of global solutions corresponding to small initial conditions is also investigated. Their convergence in $H^1$-norm to a well determinated stationary solution is proved.