A generalized domain for semigroup generators
HTML articles powered by AMS MathViewer
- by Michael G. Crandall PDF
- 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), 149โ158. 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.ย 157โ179. MR 0470787
- Michael G. Crandall, The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math. 12 (1972), 108โ132. 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), 265โ298. 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), 376โ418. 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), 204โ217. 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), 57โ94. MR 300166, DOI 10.1007/BF02761448
- Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508โ520. 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), 537โ543. MR 322603 โ, 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. I. Miyadera, Some remarks on semigroups of nonlinear operators, Tรดhoku Math. J. 23 (1971), 245-258.
- G. F. Webb, Continuous nonlinear perturbations of linear accretive operators in Banach spaces, J. Functional Analysis 10 (1972), 191โ203. MR 0361965, DOI 10.1016/0022-1236(72)90048-1
Additional Information
- © Copyright 1973 American Mathematical Society
- 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