On the asymptotic behavior of nonlinear semigroups and the range of accretive operators II

Abstract : It is known that certain problems in partial differential equations may be interpreted as initial value problems for ordinary differential equations in Banach spaces. When such an evolution equation is governed by an accretive operator, then its solutions give rise to a nonlinear contraction semigroup. In this paper we study certain aspects of the asymptotic behavior of nonlinear semigroups and or resolvents of accretive operators. We also derive new results on their behavior at the origin. It turns out that the behavior of a nonlinear semigroup resembles that of the resolvent of its generator both at infinity and at the origin. (Author)

[1]  Dennis F. Cudia.  The geometry of Banach spaces. Smoothness , 1964 .

[2]  S. Reich.  Convergence and approximation of nonlinear semigroups , 1980 .

[3]  S. Reich.  A solution to a problem on the asymptotic behavior of nonexpansive mppings and semigroups , 1980 .

[4]  Elon Kohlberg,et al.  Asymptotic behavior of nonexpansive mappings in normed linear spaces , 1981 .

[5]  M. Day,et al.  Normed Linear Spaces , 1960 .

[6]  S. Reich.  A nonlinear Hille-Yosida theorem in Banach spaces , 1981 .

[7]  A. Pazy,et al.  On the asymptotic behavior of semigroups of nonlinear contractions in Hilbert space , 1978 .

[8]  L. Shapley,et al.  Stochastic Games* , 1953, Proceedings of the National Academy of Sciences.

[9]  Andrew T. Plant,et al.  The differentiability of nonlinear semigroups in uniformly convex spaces , 1981 .

[10]  Simeon Reich,et al.  Product formulas, nonlinear semigroups, and accretive operators , 1980 .

[11]  Elon Kohlberg,et al.  The Asymptotic Theory of Stochastic Games , 1976, Math. Oper. Res..

[12]  Irving Leonard Glicksberg,et al.  Some geometric properties of the spheres in a normed linear space , 1958 .

[13]  F. Browder.  Normal solvability and $\phi $-accretive mappings of Banach spaces , 1972 .

[14]  S. Reich.  Asymptotic behavior of semigroups of nonlinear contractions in Banach spaces , 1976 .

[15]  Michael G. Crandall,et al.  GENERATION OF SEMI-GROUPS OF NONLINEAR TRANSFORMATIONS ON GENERAL BANACH SPACES, , 1971 .

[16]  H. Brezis,et al.  Produits infinis de resolvantes , 1978 .

[17]  M. Crandall.  A generalized domain for semigroup generators , 1973 .

[18]  Simeon Reich,et al.  Extension problems for accretive sets in Banach spaces , 1977 .

[19]  R. Rockafellar.  Monotone Operators and the Proximal Point Algorithm , 1976 .

[20]  S. Reich,et al.  Asymptotic behavior of solutions of a nonlinear evolution equation , 1981 .

[21]  S. Reich.  Strong convergence theorems for resolvents of accretive operators in Banach spaces , 1980 .

[22]  Flow-invariant domains of Hölder continuity for nonlinear semigroups , 1975 .

[23]  A. Pazy.  Asymptotic behavior of contractions in hilbert space , 1971 .

[24]  Simeon Reich,et al.  Some fixed point problems , 1974 .

[25]  A. Neyman,et al.  Asymptotic Behavior of Nonexpansive Mappings in Uniformly Convex Banach Spaces , 1981 .

[26]  Simeon Reich,et al.  Asymptotic behavior of contractions in Banach spaces , 1973 .

[27]  H. Brezis.  Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .

[28]  O. Nevanlinna.  Global iteration schemes for monotone operators , 1979 .

[29]  S. Reich.  NONLINEAR EVOLUTION EQUATIONS AND NONLINEAR ERGODIC THEOREMS , 1977 .

[30]  R. Rockafellar.  On the virtual convexity of the domain and range of a nonlinear maximal monotone operator , 1970 .