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On C∞ well-posedness of hyperbolic systems with multiplicities

Claudia Garetto and Michael Ruzhansky (UGent)
(2017) ANNALI DI MATEMATICA PURA ED APPLICATA. 196(5). p.1819-1834
Author
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Abstract
In this paper, we study first-order hyperbolic systems of any order with multiple characteristics (weakly hyperbolic) and time-dependent analytic coefficients. The main question is when the Cauchy problem for such systems is well-posed in C-infinity and in D'. We prove that the analyticity of the coefficients combined with suitable hypotheses on the eigenvalues guarantees the C-infinity well-posedness of the corresponding Cauchy problem.
Keywords
Hyperbolic equations, C-infinity well-posedness, Analytic coefficients, HOLDER CONTINUOUS COEFFICIENTS, CAUCHY-PROBLEM, TIME, EQUATIONS, RESPECT

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MLA
Garetto, Claudia, and Michael Ruzhansky. “On C∞ Well-Posedness of Hyperbolic Systems with Multiplicities.” ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 196, no. 5, 2017, pp. 1819–34, doi:10.1007/s10231-017-0639-2.
APA
Garetto, C., & Ruzhansky, M. (2017). On C∞ well-posedness of hyperbolic systems with multiplicities. ANNALI DI MATEMATICA PURA ED APPLICATA, 196(5), 1819–1834. https://doi.org/10.1007/s10231-017-0639-2
Chicago author-date
Garetto, Claudia, and Michael Ruzhansky. 2017. “On C∞ Well-Posedness of Hyperbolic Systems with Multiplicities.” ANNALI DI MATEMATICA PURA ED APPLICATA 196 (5): 1819–34. https://doi.org/10.1007/s10231-017-0639-2.
Chicago author-date (all authors)
Garetto, Claudia, and Michael Ruzhansky. 2017. “On C∞ Well-Posedness of Hyperbolic Systems with Multiplicities.” ANNALI DI MATEMATICA PURA ED APPLICATA 196 (5): 1819–1834. doi:10.1007/s10231-017-0639-2.
Vancouver
1.
Garetto C, Ruzhansky M. On C∞ well-posedness of hyperbolic systems with multiplicities. ANNALI DI MATEMATICA PURA ED APPLICATA. 2017;196(5):1819–34.
IEEE
[1]
C. Garetto and M. Ruzhansky, “On C∞ well-posedness of hyperbolic systems with multiplicities,” ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 196, no. 5, pp. 1819–1834, 2017.
@article{8585431,
  abstract     = {{In this paper, we study first-order hyperbolic systems of any order with multiple characteristics (weakly hyperbolic) and time-dependent analytic coefficients. The main question is when the Cauchy problem for such systems is well-posed in C-infinity and in D'. We prove that the analyticity of the coefficients combined with suitable hypotheses on the eigenvalues guarantees the C-infinity well-posedness of the corresponding Cauchy problem.}},
  author       = {{Garetto, Claudia and Ruzhansky, Michael}},
  issn         = {{0373-3114}},
  journal      = {{ANNALI DI MATEMATICA PURA ED APPLICATA}},
  keywords     = {{Hyperbolic equations,C-infinity well-posedness,Analytic coefficients,HOLDER CONTINUOUS COEFFICIENTS,CAUCHY-PROBLEM,TIME,EQUATIONS,RESPECT}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{1819--1834}},
  title        = {{On C∞ well-posedness of hyperbolic systems with multiplicities}},
  url          = {{http://doi.org/10.1007/s10231-017-0639-2}},
  volume       = {{196}},
  year         = {{2017}},
}
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