On higher-order semilinear parabolic equations with measures as initial data | Zendy

Victor A. Galaktionov | Zendy

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On higher-order semilinear parabolic equations with measures as initial data

Author(s) -

Victor A. Galaktionov

Publication year - 2004

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/8

Subject(s) - mathematics , order (exchange) , function (biology) , dirac (video compression format) , mathematical analysis , parabolic partial differential equation , boundary (topology) , boundary layer , mathematical physics , partial differential equation , physics , quantum mechanics , economics , evolutionary biology , neutrino , biology , thermodynamics , finance

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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