Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2001-03-31
Blow-Up and Convergence Results for a One-Dimensional Non-Local Parabolic ProblemA. Rougirel (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