Journal of Integral Equations and Applications

Abstract Hyperbolic Volterra Integrodifferential Equations

Yuhua Lin and Naoki Tanaka

Full-text: Open access

Article information

Source
J. Integral Equations Applications, Volume 10, Number 2 (1998), 195-218.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1181074221

Digital Object Identifier
doi:10.1216/jiea/1181074221

Mathematical Reviews number (MathSciNet)
MR1646833

Zentralblatt MATH identifier
0931.45011

Subjects
Primary: 45J05: Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
Secondary: 47G20: Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]

Keywords
Banach space Volterra integrodifferential equation nondense domain evolution operator third kind boundary condition variation of constants formula

Citation

Lin, Yuhua; Tanaka, Naoki. Abstract Hyperbolic Volterra Integrodifferential Equations. J. Integral Equations Applications 10 (1998), no. 2, 195--218. doi:10.1216/jiea/1181074221. https://projecteuclid.org/euclid.jiea/1181074221


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References

  • G. Da Prato and E. Sinestrari, Differential operators with non dense domain, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 14 (1987), 285-344.
  • R. Grimmer and E. Sinestrari, Maximum norm in one-dimensional hyperbolic problems, Differential Integral Equations 5 (1992), 421-432.
  • M.L. Heard, An abstract semilinear hyperbolic Volterra integrodifferential equation, J. Math. Anal. Appl. 80 (1981), 175-202.
  • --------, A class of hyperbolic Volterra integrodifferential equations, Nonlinear Anal. 8 (1984), 79-93.
  • W.J. Hrusa, Global existence and asymptotic stability for a semilinear hyperbolic Volterra equation with large initial data, SIAM J. Math. Anal. 16 (1985), 110-134.
  • T. Kato, On linear differential equations in Banach spaces, Comm. Pure Appl. Math. 9 (1956), 479-486.
  • --------, Linear evolution equations of ʽʽ hyperbolic" type, J. Fac. Sci. Univ. Tokyo Sect. I 17 (1970), 241-258.
  • --------, Abstract differential equations and nonlinear mixed problems, Lezioni Fermiane Accademia Nazionale dei Lincei, Scuola Normale Superiore, 1985.
  • R. Nagel and E. Sinestrari, Inhomogeneous Volterra integrodifferential equations for Hille-Yosida operators, Lecture Notes om Pure Appl. Math. 150 (1994), 51-70.
  • --------, Nonlinear hyperbolic Volterra integrodifferential equations, Nonlinear Anal. 27 (1996), 167-186.
  • N. Tanaka, Quasilinear evolution equations with non-densely defined operators, Differential Integral Equations 9 (1996), 1067-1106.