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A Remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time

Year 2017, Volume: 5 Issue: 4, 142 - 147, 01.10.2017

Abstract

We consider the inital value problem for the Klein-Gordon
equation in anti-de Sitter spacetime. We derive the pointwise decay estimate by
using the fundamental solution to the linear Klein Gordon equation in anti-de
Sitter spacetime with source term.

References

  • H. Bateman, A. Erdelyi, Higher Transcendental Functions", 1,2, McGraw-Hill, New York, 1953.
  • P. Brenner, On the existence of global smooth solutions of certain semilinear hyperbolic equations, Math. Z. 167 (2) (1979), 99–135.
  • J. Ginibre, G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math Z. 189(4) (1985), 487–505.
  • J. Ginibre, G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation II, Ann. Inst. H. Poincarè Anal. Linèaire 6(1) (1989), 15–35.
  • K. Jörgens, Das Anfangswertproblem im Grossen für eine Klasse nichtlinearer Wellengleichungen, Math. Z. 77 (1961), 295–308.
  • C. Møller, The Theory of Relativity", Clarendon Press, Oxford, 1972.
  • H. Pecher, L^p-Abschützungen und klassische Lösungen für nichtlineare Wellengleichungen. I, Math. Z. 150 (1976), 159–183.
  • K. Yagdjian, A. Galstian, The Klein-Gordon equation in anti-de Sitter spacetime, Rend. Sem. Mat. Univ. Pol. Torino 67 (2) (2009), 271–292.
  • A. Galstian, L^p-L^q Decay estimates for the Klein-Gordon equation in anti-de Sitter space–time, Rend. Istit. Mat. Univ. Trieste 42 (2010), 27–50.
  • W. von Wahl, L^p-decay rates for homogeneous wave-equations, Math. Z. 120 (1971), 93–106.
Year 2017, Volume: 5 Issue: 4, 142 - 147, 01.10.2017

Abstract

References

  • H. Bateman, A. Erdelyi, Higher Transcendental Functions", 1,2, McGraw-Hill, New York, 1953.
  • P. Brenner, On the existence of global smooth solutions of certain semilinear hyperbolic equations, Math. Z. 167 (2) (1979), 99–135.
  • J. Ginibre, G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation, Math Z. 189(4) (1985), 487–505.
  • J. Ginibre, G. Velo, The global Cauchy problem for the nonlinear Klein-Gordon equation II, Ann. Inst. H. Poincarè Anal. Linèaire 6(1) (1989), 15–35.
  • K. Jörgens, Das Anfangswertproblem im Grossen für eine Klasse nichtlinearer Wellengleichungen, Math. Z. 77 (1961), 295–308.
  • C. Møller, The Theory of Relativity", Clarendon Press, Oxford, 1972.
  • H. Pecher, L^p-Abschützungen und klassische Lösungen für nichtlineare Wellengleichungen. I, Math. Z. 150 (1976), 159–183.
  • K. Yagdjian, A. Galstian, The Klein-Gordon equation in anti-de Sitter spacetime, Rend. Sem. Mat. Univ. Pol. Torino 67 (2) (2009), 271–292.
  • A. Galstian, L^p-L^q Decay estimates for the Klein-Gordon equation in anti-de Sitter space–time, Rend. Istit. Mat. Univ. Trieste 42 (2010), 27–50.
  • W. von Wahl, L^p-decay rates for homogeneous wave-equations, Math. Z. 120 (1971), 93–106.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Muhammet Yazici This is me

Publication Date October 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 4

Cite

APA Yazici, M. (2017). A Remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time. New Trends in Mathematical Sciences, 5(4), 142-147.
AMA Yazici M. A Remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time. New Trends in Mathematical Sciences. October 2017;5(4):142-147.
Chicago Yazici, Muhammet. “A Remark on the Decay Property for the Klein-Gordon Equation in Anti-De Sitter Space Time”. New Trends in Mathematical Sciences 5, no. 4 (October 2017): 142-47.
EndNote Yazici M (October 1, 2017) A Remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time. New Trends in Mathematical Sciences 5 4 142–147.
IEEE M. Yazici, “A Remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time”, New Trends in Mathematical Sciences, vol. 5, no. 4, pp. 142–147, 2017.
ISNAD Yazici, Muhammet. “A Remark on the Decay Property for the Klein-Gordon Equation in Anti-De Sitter Space Time”. New Trends in Mathematical Sciences 5/4 (October 2017), 142-147.
JAMA Yazici M. A Remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time. New Trends in Mathematical Sciences. 2017;5:142–147.
MLA Yazici, Muhammet. “A Remark on the Decay Property for the Klein-Gordon Equation in Anti-De Sitter Space Time”. New Trends in Mathematical Sciences, vol. 5, no. 4, 2017, pp. 142-7.
Vancouver Yazici M. A Remark on the decay property for the Klein-Gordon equation in anti-de Sitter space time. New Trends in Mathematical Sciences. 2017;5(4):142-7.