On a theorem for linear evolution equations of hyperbolic type

Kazuo KOBAYASI

doi:10.2969/jmsj/03140647

Kazuo KOBAYASI

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JOURNAL FREE ACCESS

1979 Volume 31 Issue 4 Pages 647-654

DOI https://doi.org/10.2969/jmsj/03140647

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Published: 1979 Received: January 18, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) T. Kato, Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo, Sect. I, 17 (1970), 241-258.
2) T. Kato, Linear evolution equations of “hyperbolic” type II, J. Math. Soc. Japan, 25 (1973), 648-666.
3) T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58 (1975), 181-205.
4) J. R. Dorroh, A simplified proof of a theorem of Kato on linear evolution equations, J. Math. Soc. Japan, 27 (1975), 474-478.
5) E. Hille and R. S. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ. Vol. 31, Providence, 1957.
6) S. Ishii, Linear evolution equation du/dt+A(t)u=0: A case where A(t) is strongly continuous, to appear.
7) F. J. Massey III, Abstract evolution equations and the mixed problem for symmetric hyperbolic systems, Trans. Amer. Math. Soc., 168 (1972), 165-188.
8) K. Yosida, Time dependent evolution equations in a locally convex space, Math. Ann., 162 (1965), 83-86.
9) K. Yosida, Functional analysis, Springer, 1971.

Right : [1] T. Kato, Linear evolution equations of “hyperbolic” type, J. Fac. Sci. Univ. Tokyo, Sect. I, 17 (1970), 241-258.
[2] T. Kato, Linear evolution equations of “hyperbolic” type II, J. Math. Soc. Japan, 25 (1973), 648-666.
[3] T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rational Mech. Anal., 58 (1975), 181-205.
[4] J. R. Dorroh, A simplified proof of a theorem of Kato on linear evolution equations, J. Math. Soc. Japan, 27 (1975), 474-478.
[5] E. Hille and R. S. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ. Vol. 31, Providence, 1957.
[6] S. Ishii, Linear evolution equation du/dt+A(t)u=0: A case where A(t) is strongly continuous, to appear.
[7] F. J. Massey III, Abstract evolution equations and the mixed problem for symmetric hyperbolic systems, Trans. Amer. Math. Soc., 168 (1972), 165-188.
[8] K. Yosida, Time dependent evolution equations in a locally convex space, Math. Ann., 162 (1965), 83-86.
[9] K. Yosida, Functional analysis, Springer, 1971.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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