Research Article
Year 2023,
Volume: 15 Issue: 1
,
104
-
109
,
30.06.2023
Abstract
References
- Galstian, A., Lp - Lq decay estiamtes for the Klein-Gordon equation in the anti-de Sitter space-time, Rend. Istit. Mat. Univ. Trieste 42 (2010), 27–50.
- Galstian, A., Yagdjian, K., Global in time existence of self-interacting scalar field in de Sitter spacetimes, Nonlinear Anal. Real World Appl. 34 (2017), 110–139.
- Møller, C., The Theory of Relativity, Clarendon Press, Oxford, 1972.
- Nakamura, M., The Cauchy problem for semi-linear Klein-Gordon equations in de Sitter spacetime, J. Math. Anal. Appl. 410 (2014), 445–454.
- Yagdjian, K., Galstian, A., Fundamental Solutions for Wave Equation in de Sitter Model of Universe, ISSN 1437-739X, University of Potsdam, August, Preprint 2007/06.
- Yagdjian,K., Galstian, A., Fundamental solutions for the Klein–Gordon equation in de Sitter spacetime, Comm. Math. Phys. 285 (2009), 293–344.
- Yagdjian, K., Galstian, A., The Klein–Gordon equation in anti-de Sitter spacetime, Rend. Sem. Mat. Univ. Pol. Torino 67 (2) (2009), 271–292.
- Yagdjian, K., Global existence of the scalar field in de Sitter spacetime, J. Math. Anal. Appl. 396 (2012), 323–344.
- Yagdjian, K., Global existence of the self-interacting scalar field in the de Sitter universe, J. Math. Phys. 60 (5) (2019), 051503.
- Yazici, M., A remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time , New Trends Math.Sci. 5(4) (2017), 142–147.
- Yazici, M., Decay estimates for the Klein-Gordon equation in curved spacetime, Electron. J. Differential Equations 17 (2018), 1–9.
- Wahl, W. V., Lp-decay rates for homogeneous wave-equations, Math. Z. 120 (1971), 93–106.
L$^{\infty}$ Decay Estimate for the Klein-Gordon Equation in the Anti-de Sitter Model of the Universe
Abstract
We consider the inital value problem for the Klein-Gordon equation with non-zero initial data in anti-de Sitter spacetime. $L^{\infty}$ decay estimate is derived for the solutions to the linear Klein-Gordon equations in the anti-de Sitter spacetime without source term.
References
- Galstian, A., Lp - Lq decay estiamtes for the Klein-Gordon equation in the anti-de Sitter space-time, Rend. Istit. Mat. Univ. Trieste 42 (2010), 27–50.
- Galstian, A., Yagdjian, K., Global in time existence of self-interacting scalar field in de Sitter spacetimes, Nonlinear Anal. Real World Appl. 34 (2017), 110–139.
- Møller, C., The Theory of Relativity, Clarendon Press, Oxford, 1972.
- Nakamura, M., The Cauchy problem for semi-linear Klein-Gordon equations in de Sitter spacetime, J. Math. Anal. Appl. 410 (2014), 445–454.
- Yagdjian, K., Galstian, A., Fundamental Solutions for Wave Equation in de Sitter Model of Universe, ISSN 1437-739X, University of Potsdam, August, Preprint 2007/06.
- Yagdjian,K., Galstian, A., Fundamental solutions for the Klein–Gordon equation in de Sitter spacetime, Comm. Math. Phys. 285 (2009), 293–344.
- Yagdjian, K., Galstian, A., The Klein–Gordon equation in anti-de Sitter spacetime, Rend. Sem. Mat. Univ. Pol. Torino 67 (2) (2009), 271–292.
- Yagdjian, K., Global existence of the scalar field in de Sitter spacetime, J. Math. Anal. Appl. 396 (2012), 323–344.
- Yagdjian, K., Global existence of the self-interacting scalar field in the de Sitter universe, J. Math. Phys. 60 (5) (2019), 051503.
- Yazici, M., A remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time , New Trends Math.Sci. 5(4) (2017), 142–147.
- Yazici, M., Decay estimates for the Klein-Gordon equation in curved spacetime, Electron. J. Differential Equations 17 (2018), 1–9.
- Wahl, W. V., Lp-decay rates for homogeneous wave-equations, Math. Z. 120 (1971), 93–106.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | June 30, 2023 |
| DOI | https://doi.org/10.47000/tjmcs.1105934 |
| IZ | https://izlik.org/JA76EU86XK |
| Published in Issue | Year 2023 Volume: 15 Issue: 1 |