Abstract parabolic problems with non-Lipschitz critical nonlinearities

Volume 121 / 2010

Konrad J. W/as Colloquium Mathematicum 121 (2010), 203-223 MSC: Primary 35K90; Secondary 35B33, 35A07. DOI: 10.4064/cm121-2-4


The Cauchy problem for a semilinear abstract parabolic equation is considered in a fractional power scale associated with a sectorial operator appearing in the linear main part of the equation. Existence of local solutions is proved for non-Lipschitz nonlinearities satisfying a certain critical growth condition.


  • Konrad J. W/asInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland

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