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MR1426761 (97k:35118) 35K55 (35B60) Pinsky, Ross G. Existence and nonexistence of global solutions for $u\sb t=\Delta u+a(x)u\sp p$$u\sb t=\Delta u+a(x)u\sp p$ in ${\bf R}\sp d$${\bf R}\sp d$. J. Differential Equations 133 (1997), no. 1, 152–177.

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