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On critical exponents for some quasilinear parabolic equations
Author(s) -
Levine Howard A.,
Lieberman Gary M.,
Meier Peter
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670120507
Subject(s) - mathematics , bounded function , parabolic partial differential equation , mathematical analysis , critical exponent , initial value problem , function (biology) , cauchy problem , cauchy distribution , partial differential equation , scaling , geometry , evolutionary biology , biology
We study the Cauchy problem for the quasilinear parabolic equationwhere p > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with − ⩽ s ψ′( s )/ψ( s ) ⩽ θ for some θ > 0. If 1 < p < 1 + 2/ N , there are no global positive solutions, whereas if p > 1 + 2/ N , there are global, positive solutions for small initial data.