Semilinear Cauchy Problems with Almost Sectorial Operators

Volume 55 / 2007

Tomasz Dlotko 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.

Authors

  • Tomasz DlotkoInstitute of Mathematics
    Silesian University
    40-007 Katowice, Poland
    e-mail

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