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

Yıl 2017, Cilt: 5 Sayı: 4, 142 - 147, 01.10.2017

Öz

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.

Kaynakça

  • 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.
Yıl 2017, Cilt: 5 Sayı: 4, 142 - 147, 01.10.2017

Öz

Kaynakça

  • 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.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Muhammet Yazici Bu kişi benim

Yayımlanma Tarihi 1 Ekim 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 4

Kaynak Göster

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. Ekim 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, sy. 4 (Ekim 2017): 142-47.
EndNote Yazici M (01 Ekim 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, c. 5, sy. 4, ss. 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 (Ekim 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, c. 5, sy. 4, 2017, ss. 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.