zbMATH — the first resource for mathematics

A random walk for the solution sought: remarks on the difference scheme approach to nonlinear semigroups and evolution operators. (English) Zbl 0644.47048
The author extends a previous result due to Crandall and Evans for the existence of a mild solution of the abstract Cauchy problem: \[ u'(t)+Au(t)\ni F(t,u(t)). \]
Reviewer: J.I.Diaz

47H06 Nonlinear accretive operators, dissipative operators, etc.
47H20 Semigroups of nonlinear operators
35A35 Theoretical approximation in context of PDEs
60G50 Sums of independent random variables; random walks
Full Text: DOI EuDML
[1] M.G. Crandall,An introduction to evolution governed by accretive operators, Dynamical Systems, Academic Press, New York, 1976, 131–165. · Zbl 0339.35049
[2] M.G. Crandall and L.C. Evans,On the relation of the operator +to evolution governed by accretive operators, Israel J. Math. 21 (1975), 261–278. · Zbl 0351.34037 · doi:10.1007/BF02757989
[3] M.G. Crandall and T.M. Liggett,Generation of semigroups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265–298. · Zbl 0226.47038 · doi:10.2307/2373376
[4] M.A. Freedman,Further investigation of the relation of the operator +to evolution governed by accretive operators, Houston J. Math, to appear. · Zbl 0811.35172
[5] K. Kobayasi, Y. Kobayashi and S. Oharu,Nonlinear evolution operators in Banach spaces, Osaka J. Math. 21 (1984), 281–310. · Zbl 0567.47047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.