On hyperbolic systems with time-dependent Hölder characteristics
- Author
- Claudia Garetto and Michael Ruzhansky (UGent)
- Organization
- Abstract
- n this paper, we study the well-posedness of weakly hyperbolic systems with time-dependent coefficients. We assume that the eigenvalues are low regular, in the sense that they are Holder with respect to t. In the past, these kinds of systems have been investigated by Yuzawa (J Differ Equ 219(2):363-374, 2005) and Kajitani and Yuzawa (Ann Sc Norm Super Pisa Cl Sci (5) 5(4):465-482, 2006) by employing semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform property of the eigenvalues, we improve the Gevrey well-posedness result of Yuzawa (2005) and we obtain well-posedness in spaces of ultradistributions as well. Our main idea is a reduction of the system to block Sylvester form and then the formulation of suitable energy estimates inspired by the treatment of scalar equations in Garetto and Ruzhansky (J Differ Equ 253(5):1317-1340, 2012).
- Keywords
- Hyperbolic equations, Gevrey spaces, Ultradistributions, CAUCHY-PROBLEM, CONTINUOUS COEFFICIENTS, EQUATIONS, RESPECT
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8585400
- MLA
- Garetto, Claudia, and Michael Ruzhansky. “On Hyperbolic Systems with Time-Dependent Hölder Characteristics.” ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 196, no. 1, 2017, pp. 155–64, doi:10.1007/s10231-016-0567-6.
- APA
- Garetto, C., & Ruzhansky, M. (2017). On hyperbolic systems with time-dependent Hölder characteristics. ANNALI DI MATEMATICA PURA ED APPLICATA, 196(1), 155–164. https://doi.org/10.1007/s10231-016-0567-6
- Chicago author-date
- Garetto, Claudia, and Michael Ruzhansky. 2017. “On Hyperbolic Systems with Time-Dependent Hölder Characteristics.” ANNALI DI MATEMATICA PURA ED APPLICATA 196 (1): 155–64. https://doi.org/10.1007/s10231-016-0567-6.
- Chicago author-date (all authors)
- Garetto, Claudia, and Michael Ruzhansky. 2017. “On Hyperbolic Systems with Time-Dependent Hölder Characteristics.” ANNALI DI MATEMATICA PURA ED APPLICATA 196 (1): 155–164. doi:10.1007/s10231-016-0567-6.
- Vancouver
- 1.Garetto C, Ruzhansky M. On hyperbolic systems with time-dependent Hölder characteristics. ANNALI DI MATEMATICA PURA ED APPLICATA. 2017;196(1):155–64.
- IEEE
- [1]C. Garetto and M. Ruzhansky, “On hyperbolic systems with time-dependent Hölder characteristics,” ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 196, no. 1, pp. 155–164, 2017.
@article{8585400,
abstract = {{n this paper, we study the well-posedness of weakly hyperbolic systems with time-dependent coefficients. We assume that the eigenvalues are low regular, in the sense that they are Holder with respect to t. In the past, these kinds of systems have been investigated by Yuzawa (J Differ Equ 219(2):363-374, 2005) and Kajitani and Yuzawa (Ann Sc Norm Super Pisa Cl Sci (5) 5(4):465-482, 2006) by employing semigroup techniques (Tanabe-Sobolevski method). Here, under a certain uniform property of the eigenvalues, we improve the Gevrey well-posedness result of Yuzawa (2005) and we obtain well-posedness in spaces of ultradistributions as well. Our main idea is a reduction of the system to block Sylvester form and then the formulation of suitable energy estimates inspired by the treatment of scalar equations in Garetto and Ruzhansky (J Differ Equ 253(5):1317-1340, 2012).}},
author = {{Garetto, Claudia and Ruzhansky, Michael}},
issn = {{0373-3114}},
journal = {{ANNALI DI MATEMATICA PURA ED APPLICATA}},
keywords = {{Hyperbolic equations,Gevrey spaces,Ultradistributions,CAUCHY-PROBLEM,CONTINUOUS COEFFICIENTS,EQUATIONS,RESPECT}},
language = {{eng}},
number = {{1}},
pages = {{155--164}},
title = {{On hyperbolic systems with time-dependent Hölder characteristics}},
url = {{http://doi.org/10.1007/s10231-016-0567-6}},
volume = {{196}},
year = {{2017}},
}
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