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Semilinear Cauchy problems with almost sectorial operators

Dlotko T.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 4

333-346

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 Holder spaces illustrates the abstract result.

On approximation of (1.A) semigroups by discrete semigroups

Bobrowski A.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

141-154

A generalization of a recent result of N. Tanaka concerning approximation by "integrated" discrete semigroups is presented.