Abstract
For a semilinear parabolic initial boundary value problem we establish criterions on blow-up of the solution in finite time and give bounds for the blow-up time. We treat several applications in both finite and infinite domains. For comparison, sufficient conditions are also given for the existence of global solutions.
Zusammenfassung
Für ein semilineares parabolisches Rand- und Anfangswertproblem stellen wir Kriterien für die Explosion der Lösung in endlicher Zeit auf und geben Schranken für die Explosionszeit an. Einige Anwendungen in beschränkten und unbeschränkten Gebieten werden untersucht, wobei wir als Gegenüberstellung auch hinreichende Bedingungen für die Existenz globaler Lösungen angeben.
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Meier, P. Blow-up of solutions of semilinear parabolic differential equations. Z. angew. Math. Phys. 39, 135–149 (1988). https://doi.org/10.1007/BF00945760
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DOI: https://doi.org/10.1007/BF00945760