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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

##### MSC:
 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
##### Keywords:
mild solution of the abstract Cauchy problem
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##### References:
 [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
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