Abstract parabolic problems with non-Lipschitz critical nonlinearities
Volume 121 / 2010
Colloquium Mathematicum 121 (2010), 203-223
MSC: Primary 35K90; Secondary 35B33, 35A07.
DOI: 10.4064/cm121-2-4
Abstract
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.
