A generalized domain for semigroup generators

Crandall, Michael G.

doi:10.1090/S0002-9939-1973-0313873-1

A generalized domain for semigroup generators
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Proc. Amer. Math. Soc. 37 (1973), 434-440 Request permission

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.

References

B. Calvert and K. Gustafson, Multiplicative perturbation of nonlinear $m$-accretive operators, J. Functional Analysis 10 (1972), 149–158. MR 0341200, DOI 10.1016/0022-1236(72)90046-8
Michael G. Crandall, Semigroups of nonlinear transformations in Banach spaces, Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971) Publ. Math. Res. Center Univ. Wisconsin, No. 27, Academic Press, New York, 1971, pp. 157–179. MR 0470787
Michael G. Crandall, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math. 12 (1972), 108–132. MR 316925, DOI 10.1007/BF02764657
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 287357, DOI 10.2307/2373376
Michael G. Crandall and Amnon Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Functional Analysis 3 (1969), 376–418. MR 0243383, DOI 10.1016/0022-1236(69)90032-9
Michael G. Crandall and Amnon Pazy, On accretive sets in Banach spaces, J. Functional Analysis 5 (1970), 204–217. MR 0259563, DOI 10.1016/0022-1236(70)90026-1
M. G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, Israel J. Math. 11 (1972), 57–94. MR 300166, DOI 10.1007/BF02761448
Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508–520. MR 226230, DOI 10.2969/jmsj/01940508
Yoshio Konishi, Some examples of nonlinear semi-groups in Banach lattices, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 18 (1971/72), 537–543. MR 322603

On

and the differentiability of the nonlinear semi-group associated with it

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Some remarks on semigroups of nonlinear operators

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G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Functional Analysis 10 (1972), 191–203. MR 0361965, DOI 10.1016/0022-1236(72)90048-1