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A generalized domain for semigroup generators


Author: Michael G. Crandall
Journal: Proc. Amer. Math. Soc. 37 (1973), 434-440
MSC: Primary 47D05; Secondary 47H99
DOI: https://doi.org/10.1090/S0002-9939-1973-0313873-1
MathSciNet review: 0313873
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Abstract: A generalized domain $ \hat D(A)$ is assigned to a certain class of generators A of semigroups of nonlinear transformations S on Banach spaces. $ \hat D(A)$ is then characterized in two ways. $ \hat D(A)$ is the set of x such that $ S(t)x$ is locally Lipschitz continuous in t or, equivalently, the set of x which can lie in the domain of suitable extensions of A.


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  • [1] B. Calvert and K. Gustafson, Multiplicative perturbation of nonlinear m-accretive operators, J. Functional Analysis 10 (1972), 149-157. MR 0341200 (49:5950)
  • [2] M. G. Crandall, Semigroups of nonlinear transformations in Banach spaces, Contributions to Nonlinear Functional Analysis, Eduardo H. Zarantonello (Editor), Academic Press, New York, 1971, pp. 157-179. MR 0470787 (57:10532)
  • [3] -, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math. (to appear). MR 0316925 (47:5473)
  • [4] M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265-298. MR 0287357 (44:4563)
  • [5] M. G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Functional Analysis 3 (1969), 376-418. MR 39 #4705. MR 0243383 (39:4705)
  • [6] -, On accretive sets in Banach spaces, J. Functional Analysis 5 (1970), 204-217. MR 41 #4201. MR 0259563 (41:4201)
  • [7] -, Nonlinear evolution equations in Banach spaces, Israel J. Math. 11 (1972), 57-94. MR 0300166 (45:9214)
  • [8] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520. MR 37 #1820. MR 0226230 (37:1820)
  • [9] Y. Konishi, Some examples of nonlinear semi-groups in Banach lattices, J. Fac. Sci. Univ. Tokyo Sect. IA 18 (1972), 537-543. MR 0322603 (48:965)
  • [10] -, On $ {u_t} = {u_{xx}} - F({u_x})$ and the differentiability of the nonlinear semi-group associated with it, Proc. Japan Acad. 48 (1972), 281-286.
  • [11] I. Miyadera, Some remarks on semigroups of nonlinear operators, Tôhoku Math. J. 23 (1971), 245-258.
  • [12] G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Functional Analysis 10 (1972), 191-203. MR 0361965 (50:14407)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313873-1
Article copyright: © Copyright 1973 American Mathematical Society

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