Semilinear Cauchy Problems with Almost Sectorial Operators
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 333-346
MSC: 35A07, 35K90, 37L05.
DOI: 10.4064/ba55-4-5
Abstract
Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Hölder spaces illustrates the abstract result.
