Abstract
Abstract Let Ω be an open bounded subset of ℝN and b a measurable nonnegative function in ℝ. We study the time compact support property for ∂tu - Δpu + b(x)uq = 0 with p > 2 and for ∂tu - Δ(um) + b(x)uq = 0 with m > 1 where 0 ≤ q < 1. Some criteria involving the asymptotics as h → 0 of the first eigenvalue of are given which imply such a phenomenon. Applying these criteria we deduce that the time vanishing property occurs when 1/b belongs to Ls(Ω) for some s depending on q, and p or m.
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