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MR1937838 35K55 (35K10)
Benachour, S.; Laurençot, Ph.; Schmitt, D.; Souplet, Ph. Extinction and non-extinction for viscous Hamilton-Jacobi equations in $\Bbb R^N$. Asymptot. Anal. 31 (2002), no. 3-4, 229–246.
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