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 -norm to a well determinated stationary solution is proved.
Cite this article
A. Rougirel, Blow-Up and Convergence Results for a One-Dimensional Non-Local Parabolic Problem. Z. Anal. Anwend. 20 (2001), no. 1, pp. 93–113DOI 10.4171/ZAA/1005