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MR1835063 (2002j:35149) 35K55 (35B35 35B45 47D06 47N20)
Fila, Marek; Souplet, Philippe; Weissler, Fred B. Linear and nonlinear heat equations in $L\sp q\sb \delta$ spaces and universal bounds for global solutions. Math. Ann. 320 (2001), no. 1, 87–113.
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