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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 1, 2001, pp. 93–113
DOI: 10.4171/ZAA/1005

Published online: 2001-03-31

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

A. Rougirel[1]

(1) Universität Zürich, Switzerland

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.

Keywords: Parabolic problems, blow-up, convergence to steady states

Rougirel A.: Blow-Up and Convergence Results for a One-Dimensional Non-Local Parabolic Problem. Z. Anal. Anwend. 20 (2001), 93-113. doi: 10.4171/ZAA/1005