Abstract
We consider 2mth-order (m 2) semilinear parabolic equations ut = ( 1) m u ± |u| p 1 u in R N ◊ R+ (p > 1), with Dirac's mass (x) as the initial function. We show that for p 0, while for p p0 such a local in time solution does not exist. This leads to a boundary layer phenomenon in constructing a proper solution via regular approximations.
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