Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups
- Author
- Arun Kumar Bhardwaj, Vishvesh Kumar (UGent) and Shyam Swarup Mondal
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- Project
- Abstract
- Let G be a compact Lie group. In this article, we investigate the Cauchy problem for a nonlinear wave equation with the viscoelastic damping on G. More precisely, we investigate some L2-estimates for the solution to the homogeneous nonlinear viscoelastic damped wave equation on G utilizing the group Fourier transform on G. We also prove that there is no improvement of any decay rate for the norm || u(t, center dot)|| L-2( G) by further assuming the L-1(G)-regularity of initial data. Finally, using the noncommutative Fourier analysis on compact Lie groups, we prove a local in time existence result in the energy space C-1([ 0, T], H-L(1) (G)).
- Keywords
- ‘Ghent Analysis & PDE center, nonlinear wave equation, viscoelastic damping, L-2-L-2-estimate, local well-posedness, compact Lie groups, ASYMPTOTIC PROFILES, CRITICAL EXPONENT, L-P, DECAY
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01H0XD67TGQ3K1V9KEF7GJ0DS4
- MLA
- Bhardwaj, Arun Kumar, et al. “Estimates for the Nonlinear Viscoelastic Damped Wave Equation on Compact Lie Groups.” PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, vol. 154, no. 3, 2024, pp. 810–29, doi:10.1017/prm.2023.38.
- APA
- Bhardwaj, A. K., Kumar, V., & Mondal, S. S. (2024). Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 154(3), 810–829. https://doi.org/10.1017/prm.2023.38
- Chicago author-date
- Bhardwaj, Arun Kumar, Vishvesh Kumar, and Shyam Swarup Mondal. 2024. “Estimates for the Nonlinear Viscoelastic Damped Wave Equation on Compact Lie Groups.” PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS 154 (3): 810–29. https://doi.org/10.1017/prm.2023.38.
- Chicago author-date (all authors)
- Bhardwaj, Arun Kumar, Vishvesh Kumar, and Shyam Swarup Mondal. 2024. “Estimates for the Nonlinear Viscoelastic Damped Wave Equation on Compact Lie Groups.” PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS 154 (3): 810–829. doi:10.1017/prm.2023.38.
- Vancouver
- 1.Bhardwaj AK, Kumar V, Mondal SS. Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS. 2024;154(3):810–29.
- IEEE
- [1]A. K. Bhardwaj, V. Kumar, and S. S. Mondal, “Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups,” PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, vol. 154, no. 3, pp. 810–829, 2024.
@article{01H0XD67TGQ3K1V9KEF7GJ0DS4,
abstract = {{Let G be a compact Lie group. In this article, we investigate the Cauchy problem for a nonlinear wave equation with the viscoelastic damping on G. More precisely, we investigate some L2-estimates for the solution to the homogeneous nonlinear viscoelastic damped wave equation on G utilizing the group Fourier transform on G. We also prove that there is no improvement of any decay rate for the norm || u(t, center dot)|| L-2( G) by further assuming the L-1(G)-regularity of initial data. Finally, using the noncommutative Fourier analysis on compact Lie groups, we prove a local in time existence result in the energy space C-1([ 0, T], H-L(1) (G)).}},
author = {{Bhardwaj, Arun Kumar and Kumar, Vishvesh and Mondal, Shyam Swarup}},
issn = {{0308-2105}},
journal = {{PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS}},
keywords = {{‘Ghent Analysis & PDE center,nonlinear wave equation,viscoelastic damping,L-2-L-2-estimate,local well-posedness,compact Lie groups,ASYMPTOTIC PROFILES,CRITICAL EXPONENT,L-P,DECAY}},
language = {{eng}},
number = {{3}},
pages = {{810--829}},
title = {{Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups}},
url = {{http://doi.org/10.1017/prm.2023.38}},
volume = {{154}},
year = {{2024}},
}
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