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Approximation of nonlinear semigroups and evolution equations
Jerome A. GOLDSTEIN
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Jerome A. GOLDSTEIN
Department of Mathematics Tulane University
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1972 Volume 24 Issue 4 Pages 558-573
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- Published: 1972 Received: September 23, 1971 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Brezis, M. G. Crandall and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach space, Comm. Pure Appl. Math., 23 (1970), 123-144.
2) H. Brezis and A. Pazy, Semigroups of nonlinear contractions on convex sets, J. Functional Analysis, 6 (1970), 237-281.
3) P. R. Chernoff, Semigroup Product Formulas and Addition of Unbounded Operators, Ph. D. Thesis, Harvard Univ., 1968.
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.
5) M. G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Functional Analysis, 3 (1969), 376-418.
6) J. A. Goldstein, Semigroups of Operators and Abstract Cauchy Problems, Tulane University Lecture Notes, 1970.
7) J. A. Goldstein, Some counterexamples involving self-adjoint operators, Rocky Mtn. Math. J. (to appear).
8) T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
9) T. Kato, Approximation theorems for evolution equations, Lectures in Differential Equations, Volume II, Van Nostrand Reinhold, New York (1969), 115-124.
10) T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math., 18, Part I, Amer. Math. Soc., Providence, R. I., 1970, 138-161.
11) J. Kisynski, A proof of the Trotter-Kato theorem on approximation of semigroups, Coll. Math., 18 (1967), 181-184.
12) R. H. Martin, Jr., The logarithmic derivative and equations of evolution in a Banach space, J. Math. Soc. Japan, 22 (1970), 411-429.
13) R. H. Martin, Jr., A global existence theorem for autonomous differential equations in a Banach space, Proc. Amer. Math. Soc., 26 (1970), 307-314.
14) J. Mermin, An exponential limit formula for nonlinear semigroups, Trans. Amer. Math. Soc., 150 (1970), 469-476.
15) I. Miyadera, On the convergence of nonlinear semi-groups, Tôhoku Math. J., 21 (1969), 221-236.
16) I. Miyadera, On the convergence of nonlinear semi-groups II, J. Math. Soc. Japan, 21 (1969), 403-412.
17) I. Miyadera and S. Oharu, Approximation of semi-groups of nonlinear operators, to appear.
18) A. Pazy, Semi-groups of nonlinear contractions in Hilbert space, Problems in Non-linear Analysis, Edizione Cremonese, Rome, 1971, 343-430.
19) I. Singer, Linear functionals on the space of continuous mappings of a compact space into a Banach space (in Russian), Revue Math. Pures et Appl., 2 (1957), 301-315.
20) I. Singer, Les duals des certain espaces de Banach de champs de vecteurs, I, II, Bull. Sci. Math., 82 (1958), 29-40; 83 (1959), 73-96.
21) R. A. Struble, Nonlinear Differential Equations, McGraw-Hill, New York, 1962.
22) G. F. Webb, Nonlinear evolution equations and product integration in Banach spaces, Trans. Amer. Math. Soc., 148 (1970), 273-282.
23) P. Bénilan, Une remarque sur la convergence des semi-groupes non linéaires, C. R. Acad. Sc. Paris, 272 (1971), 1182-1184.
24) H. Brezis, On a problem of T. Kato, Comm. Pure Appl. Math., 24 (1971), 1-6.
25) H. Brezis and A. Pazy, Convergence and approximation of semigroups of non linear operators in Banach spaces, J. Functional Analysis, to appear.
26) M. G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, to appear.
27) W. E. Fitzgibbon, Approximation of nonlinear evolution equations, to appear.
28) W.E. Fitzgibbon, Time dependent nonlinear Cauchy problems in Banach spaces, to appear.
29) R. H. Martin, Jr., Generating an evolution system in a class of uniformly convex Banach spaces, to appear.
30) I. Miyadera, Some remarks on semi-groups of nonlinear operators, Tohoku Math. J., 23 (1971), 245-258.
Right : [1] H. Brezis, M. G. Crandall and A. Pazy, Perturbations of nonlinear maximal monotone sets in Banach space, Comm. Pure Appl. Math., 23 (1970), 123-144.
[2] H. Brezis and A. Pazy, Semigroups of nonlinear contractions on convex sets, J. Functional Analysis, 6 (1970), 237-281.
[3] P. R. Chernoff, Semigroup Product Formulas and Addition of Unbounded Operators, Ph. D. Thesis, Harvard Univ., 1968.
[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.
[5] M. G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets, J. Functional Analysis, 3 (1969), 376-418.
[6] J. A. Goldstein, Semigroups of Operators and Abstract Cauchy Problems, Tulane University Lecture Notes, 1970.
[7] J. A. Goldstein, Some counterexamples involving self-adjoint operators, Rocky Mtn. Math. J. (to appear).
[8] T. Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan, 19 (1967), 508-520.
[9] T. Kato, Approximation theorems for evolution equations, Lectures in Differential Equations, Volume II, Van Nostrand Reinhold, New York (1969), 115-124.
[10] T. Kato, Accretive operators and nonlinear evolution equations in Banach spaces, Proc. Symp. Pure Math., 18, Part I, Amer. Math. Soc., Providence, R. I., 1970, 138-161.
[11] J. Kisynski, A proof of the Trotter-Kato theorem on approximation of semigroups, Coll. Math., 18 (1967), 181-184.
[12] R. H. Martin, Jr., The logarithmic derivative and equations of evolution in a Banach space, J. Math. Soc. Japan, 22 (1970), 411-429.
[13] R. H. Martin, Jr., A global existence theorem for autonomous differential equations in a Banach space, Proc. Amer. Math. Soc., 26 (1970), 307-314.
[14] J. Mermin, An exponential limit formula for nonlinear semigroups, Trans. Amer. Math. Soc., 150 (1970), 469-476.
[15] I. Miyadera, On the convergence of nonlinear semi-groups, Tôhoku Math. J., 21 (1969), 221-236.
[16] I. Miyadera, On the convergence of nonlinear semi-groups II, J. Math. Soc. Japan, 21 (1969), 403-412.
[17] I. Miyadera and S. Ôharu, Approximation of semi-groups of nonlinear operators, to appear.
[18] A. Pazy, Semi-groups of nonlinear contractions in Hilbert space, Problems in Non-linear Analysis, Edizione Cremonese, Rome, 1971, 343-430.
[19] I. Singer, Linear functionals on the space of continuous mappings of a compact space into a Banach space (in Russian), Revue Math. Pures et Appl., 2 (1957), 301-315.
[20] I. Singer, Les duals des certain espaces de Banach de champs de vecteurs, I, II, Bull. Sci. Math., 82 (1958), 29-40; 83 (1959), 73-96.
[21] R. A. Struble, Nonlinear Differential Equations, McGraw-Hill, New York, 1962.
[22] G. F. Webb, Nonlinear evolution equations and product integration in Banach spaces, Trans. Amer. Math. Soc., 148 (1970), 273-282.
[23] P. Bénilan, Une remarque sur la convergence des semi-groupes non linéaires, C. R. Acad. Sc. Paris, 272 (1971), 1182-1184.
[24] H. Brezis, On a problem of T. Kato, Comm. Pure Appl. Math., 24 (1971), 1-6.
[25] H. Brezis and A. Pazy, Convergence and approximation of semigroups of nonlinear operators in Banach spaces, J. Functional Analysis, to appear.
[26] M. G. Crandall and A. Pazy, Nonlinear evolution equations in Banach spaces, to appear.
[27] W. E. Fitzgibbon, Approximation of nonlinear evolution equations, to appear.
[28] W.E. Fitzgibbon, Time dependent nonlinear Cauchy problems in Banach spaces, to appear.
[29] R. H. Martin, Jr., Generating an evolution system in a class of uniformly convex Banach spaces, to appear.
[30] I. Miyadera, Some remarks on semi-groups of nonlinear operators, Tôhoku Math. J., 23 (1971), 245-258.
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