Skip to Main Content

Sugaku Expositions

Sugaku Expositions contains translations into English of expository articles from the journal Sugaku, published by Iwanami Shoten, publishers for the Mathematical Society of Japan. Published biannually, each issue of Sugaku Expositions contains several expository articles that provide highly informative accounts of a variety of current areas of research.

ISSN 2473-585X (online) ISSN 0898-9583 (print)

The 2020 MCQ for Sugaku Expositions is 0.14.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Theory of Hyperbolic Evolution Equations and Partial Differential Equations
HTML articles powered by AMS MathViewer

by Yoshio Tsutsumi
Translated by: Satoshi Tonegawa
Sugaku Expositions 32 (2019), 137-153
DOI: https://doi.org/10.1090/suga/441
Published electronically: September 26, 2019
References
  • J. Bourgain, Global solutions of nonlinear Schrödinger equations, American Mathematical Society Colloquium Publications, vol. 46, American Mathematical Society, Providence, RI, 1999. MR 1691575, DOI 10.1090/coll/046
  • H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert, North-Holland Math. Stud., 5, North-Holland Publishing, Amsterdam-London, 1973.
  • Michael G. Crandall and Panagiotis E. Souganidis, Convergence of difference approximations of quasilinear evolution equations, Nonlinear Anal. 10 (1986), no. 5, 425–445. MR 839356, DOI 10.1016/0362-546X(86)90049-0
  • Robert Denk, Matthias Hieber, and Jan Prüss, $\scr R$-boundedness, Fourier multipliers and problems of elliptic and parabolic type, Mem. Amer. Math. Soc. 166 (2003), no. 788, viii+114. MR 2006641, DOI 10.1090/memo/0788
  • Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
  • K. O. Friedrichs, The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc. 55 (1944), 132–151. MR 9701, DOI 10.1090/S0002-9947-1944-0009701-0
  • K. O. Friedrichs, Symmetric hyperbolic linear differential equations, Comm. Pure Appl. Math. 7 (1954), 345–392. MR 62932, DOI 10.1002/cpa.3160070206
  • Hiroshi Fujita and Tosio Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16 (1964), 269–315. MR 166499, DOI 10.1007/BF00276188
  • Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244
  • Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, New York, 1948. MR 0025077
  • Susumu Ishii, Linear evolution equations $du/dt+A(t)u=0$ : a case where $A(t)$ is strongly uniform-measurable, J. Math. Soc. Japan 34 (1982), no. 3, 413–424. MR 659612, DOI 10.2969/jmsj/03430413
  • Tosio Kato, Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo Sect. I 17 (1970), 241–258. MR 279626
  • Tosio Kato, Linear evolution equations of “hyperbolic” type. II, J. Math. Soc. Japan 25 (1973), 648–666. MR 326483, DOI 10.2969/jmsj/02540648
  • T. Kato, Quasi-linear equations of evolution, with applications to partial differential equations, Spectral Theory and Differential Equations, Proceedings of the Symposium, Dundee, 1974, Dedicated to the life, word and memory of Konrad Jörgens, (ed. W. N. Everitt), Lecture Notes in Math., 448, Springer, 1975, 25-70.
  • T. Kato, Abstract differential equations and nonlinear mixed problems, Lezioni Fermiane. [Fermi Lectures], Scuola Normale Superiore, Pisa; Accademia Nazionale dei Lincei, Rome, 1985. MR 930267
  • T. Kato, On nonlinear Schrödinger equations, Ann. Insti. H. Poincaré, Phys. Théor., 46 (1987), 113-129.
  • Kazuo Kobayasi, On a theorem for linear evolution equations of hyperbolic type, J. Math. Soc. Japan 31 (1979), no. 4, 647–654. MR 544682, DOI 10.2969/jmsj/03140647
  • Kazuo Kobayasi and Nobuhiro Sanekata, A method of iterations for quasi-linear evolution equations in nonreflexive Banach spaces, Hiroshima Math. J. 19 (1989), no. 3, 521–540. MR 1035141
  • Yukio K\B{o}mura, Nonlinear semi-groups in Hilbert space, J. Math. Soc. Japan 19 (1967), 493–507. MR 216342, DOI 10.2969/jmsj/01940493
  • A. Majda, Compressible fluid flow and systems of conservation laws in several space variables, Applied Mathematical Sciences, vol. 53, Springer-Verlag, New York, 1984. MR 748308, DOI 10.1007/978-1-4612-1116-7
  • K. Masuda, Evolution Equations, Kinokuniya Sugaku Sosho, 6, Kinokuniya Co. Ltd., 1975. (Japanese)
  • Isao Miyadera, Nonlinear semigroups, Translations of Mathematical Monographs, vol. 109, American Mathematical Society, Providence, RI, 1992. Translated from the 1977 Japanese original by Choong Yun Cho. MR 1192132, DOI 10.1090/mmono/109
  • I. Miyadera, Functional analysis, 2nd ed., Rikogakusha Publishing Co. Ltd., 1996. (Japanese)
  • S. Mizohata, Theory of Partial Differential Equations, Iwanami Shoten, Publishers, 1965. (Japanese)
  • Kenji Nakanishi and Wilhelm Schlag, Invariant manifolds and dispersive Hamiltonian evolution equations, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2011. MR 2847755, DOI 10.4171/095
  • Noboru Okazawa, Remarks on linear evolution equations of hyperbolic type in Hilbert space, Adv. Math. Sci. Appl. 8 (1998), no. 1, 399–423. MR 1623319
  • I. G. Petrovsky, Lectures on partial differential equations, Interscience Publishers, New York-London, 1954. Translated by A. Shenitzer. MR 0065760
  • Nobuhiro Sanekata, Abstract quasi-linear equations of evolution in nonreflexive Banach spaces, Hiroshima Math. J. 19 (1989), no. 1, 109–139. MR 1009665
  • Irving Segal, Non-linear semi-groups, Ann. of Math. (2) 78 (1963), 339–364. MR 152908, DOI 10.2307/1970347
  • H. Tanabe, Evolution Equations, Iwanami Shoten, Publishers, 1975. (Japanese)
  • Terence Tao, Nonlinear dispersive equations, CBMS Regional Conference Series in Mathematics, vol. 106, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006. Local and global analysis. MR 2233925, DOI 10.1090/cbms/106
  • Y. Tsutsumi, Theory of Evolution Equations and “Hyperbolic” Partial Differential Equations, Proceedings of the 13th Evolution Equation Seminar for Young Mathematicians, Joint Research Center for Science and Technology, Ryukoku University, 1992, 1-40. (Japanese)
  • Kôsaku Yosida, On the differentiability and the representation of one-parameter semi-group of linear operators, J. Math. Soc. Japan 1 (1948), 15–21. MR 28537, DOI 10.2969/jmsj/00110015
  • Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913
Similar Articles
  • Retrieve articles in Sugaku Expositions with MSC (2010): 35-02, 35A24
  • Retrieve articles in all journals with MSC (2010): 35-02, 35A24
Bibliographic Information
  • Yoshio Tsutsumi
  • Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
  • Email: tsutsumi@math.kyoto-u.ac.jp
  • Published electronically: September 26, 2019
  • © Copyright 2019 American Mathematical Society
  • Journal: Sugaku Expositions 32 (2019), 137-153
  • MSC (2010): Primary 35-02; Secondary 35A24
  • DOI: https://doi.org/10.1090/suga/441
  • MathSciNet review: 4018215