Bulletin of the American Mathematical Society

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Book Information:

Authors: Alberto Cialdea and Vladimir Maz’ya
Title: Semi-bounded differential operators, contractive semigroups, and beyond
Additional book information: Operator Theory: Advances and Applications, Vol. 243, Birkh\"auser/Springer, Cham, Switzerland, 2014, xiv+252 pp., ISBN 978-3-319-04557-3

Adam Bobrowski, Convergence of one-parameter operator semigroups, New Mathematical Monographs, vol. 30, Cambridge University Press, Cambridge, 2016. In models of mathematical biology and elsewhere. MR 3526064, DOI 10.1017/CBO9781316480663

Edward Brian Davies, One-parameter semigroups, London Mathematical Society Monographs, vol. 15, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. MR 591851

Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162

Klaus-Jochen Engel and Rainer Nagel, One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol. 194, Springer-Verlag, New York, 2000. With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt. MR 1721989

Hector O. Fattorini, The Cauchy problem, Encyclopedia of Mathematics and its Applications, vol. 18, Addison-Wesley Publishing Co., Reading, Mass., 1983. With a foreword by Felix E. Browder. MR 692768

Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Enrico Obrecht, and Silvia Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem, Math. Nachr. 283 (2010), no. 4, 504–521. MR 2649366, DOI 10.1002/mana.200910086

J. A. Goldstein, Semigroups of linear operators and applications, Oxford University Press, Oxford and New York, 1985. Second enlarged edition, Dover Publications, 2017.

Changfeng Gui, Wei-Ming Ni, and Xuefeng Wang, On the stability and instability of positive steady states of a semilinear heat equation in $\textbf {R}^n$, Comm. Pure Appl. Math. 45 (1992), no. 9, 1153–1181. MR 1177480, DOI 10.1002/cpa.3160450906

Changfeng Gui, Wei-Ming Ni, and Xuefeng Wang, Further study on a nonlinear heat equation, J. Differential Equations 169 (2001), no. 2, 588–613. Special issue in celebration of Jack K. Hale’s 70th birthday, Part 4 (Atlanta, GA/Lisbon, 1998). MR 1808476, DOI 10.1006/jdeq.2000.3909

Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, New York, 1948. MR 0025077

Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373

Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473

S. G. Kreĭn, Linear differential equations in Banach space, Translations of Mathematical Monographs, Vol. 29, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin. MR 0342804

Peter D. Lax, Functional analysis, Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], New York, 2002. MR 1892228

A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1

Horng-Tzer Yau, The work of Cédric Villani, Proceedings of the International Congress of Mathematicians. Volume I, Hindustan Book Agency, New Delhi, 2010, pp. 87–98. MR 2827884

Kôsaku Yosida, Functional analysis, Die Grundlehren der mathematischen Wissenschaften, Band 123, Academic Press, Inc., New York; Springer-Verlag, Berlin, 1965. MR 0180824

• Adam Bobrowski, Convergence of one-parameter operator semigroups in models of mathematical biology and elsewhere, New Mathematical Monographs, vol. 30, Cambridge University Press, Cambridge, 2016. MR 3526064, DOI 10.1017/CBO9781316480663
• E. Brian Davies, One-parameter semigroups, London Mathematical Society Monographs, vol. 15, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London–New York, 1980. MR 591851
• Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I. General theory, Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1988. With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original. MR 1009162
• Klaus-Jochen Engel and Rainer Nagel, One-parameter semigroups for linear evolution equations, Graduate Texts in Mathematics, vol. 194, Springer-Verlag, New York, 2000. With contributions by S. Brendle, M. Campiti, T. Hahn, G. Metafune, G. Nickel, D. Pallara, C. Perazzoli, A. Rhandi, S. Romanelli and R. Schnaubelt. MR 1721989
• Hector O. Fattorini, The Cauchy problem, Encyclopedia of Mathematics and its Applications, vol. 18, Addison-Wesley Publishing Co., Reading, Mass., 1983. With a foreword by Felix E. Browder. MR 692768
• Angelo Favini, Gisèle Ruiz Goldstein, Jerome A. Goldstein, Enrico Obrecht, and Silvia Romanelli, Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem, Math. Nachr. 283 (2010), no. 4, 504–521. MR 2649366, DOI 10.1002/mana.200910086
• J. A. Goldstein, Semigroups of linear operators and applications, Oxford University Press, Oxford and New York, 1985. Second enlarged edition, Dover Publications, 2017.
• Changfeng Gui, Wei-Ming Ni, and Xuefeng Wang, On the stability and instability of positive steady states of a semilinear heat equation in $\textbf {R}^n$, Comm. Pure Appl. Math. 45 (1992), no. 9, 1153–1181. MR 1177480, DOI 10.1002/cpa.3160450906
• Changfeng Gui, Wei-Ming Ni, and Xuefeng Wang, Further study on a nonlinear heat equation, J. Differential Equations 169 (2001), no. 2, 588–613. MR 1808476, DOI 10.1006/jdeq.2000.3909
• Einar Hille, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, New York, 1948. MR 0025077
• Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
• Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
• S. G. Kreĭn, Linear differential equations in Banach space, Translations of Mathematical Monographs, Vol. 29; Translated from the Russian by J. M. Danskin, American Mathematical Society, Providence, R.I., 1971. MR 0342804
• Peter D. Lax, Functional analysis, Pure and Applied Mathematics (New York), Wiley-Interscience [John Wiley & Sons], New York, 2002. MR 1892228
• A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486, DOI 10.1007/978-1-4612-5561-1
• Horng-Tzer Yau, The work of Cédric Villani, Proceedings of the International Congress of Mathematicians. Volume I, Hindustan Book Agency, New Delhi, 2010, pp. 87–98. MR 2827884
• Kôsaku Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften, Band 123, Academic Press, Inc., New York; Springer-Verlag, Berlin, 1965. MR 0180824