Tsuchiya, Takuya; Nakamura, Makoto Numerical accuracy and stability of semilinear Klein-Gordon equation in de Sitter spacetime. (English) Zbl 07780407 JSIAM Lett. 15, 45-48 (2023). MSC: 65N06 PDFBibTeX XMLCite \textit{T. Tsuchiya} and \textit{M. Nakamura}, JSIAM Lett. 15, 45--48 (2023; Zbl 07780407) Full Text: DOI arXiv
Palmieri, Alessandro Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter Spacetime. (English) Zbl 1523.35074 Appl. Anal. 102, No. 13, 3577-3608 (2023). MSC: 35B44 35L15 35L71 33C10 PDFBibTeX XMLCite \textit{A. Palmieri}, Appl. Anal. 102, No. 13, 3577--3608 (2023; Zbl 1523.35074) Full Text: DOI arXiv
Ichimiya, Mikio; Nakamura, Makoto On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime. (English) Zbl 1520.35143 Evol. Equ. Control Theory 12, No. 6, 1602-1628 (2023). MSC: 35Q55 35L71 35Q75 PDFBibTeX XMLCite \textit{M. Ichimiya} and \textit{M. Nakamura}, Evol. Equ. Control Theory 12, No. 6, 1602--1628 (2023; Zbl 1520.35143) Full Text: DOI
Ebert, M. R.; Reissig, M. A note to semilinear de Sitter models in 1d with balanced mass and dissipation. (English) Zbl 1517.35133 Nonlinear Anal., Real World Appl. 71, Article ID 103835, 9 p. (2023). MSC: 35L15 35L71 PDFBibTeX XMLCite \textit{M. R. Ebert} and \textit{M. Reissig}, Nonlinear Anal., Real World Appl. 71, Article ID 103835, 9 p. (2023; Zbl 1517.35133) Full Text: DOI
Palmieri, Alessandro; Takamura, Hiroyuki On a semilinear wave equation in anti-de Sitter spacetime: the critical case. (English) Zbl 1508.35022 J. Math. Phys. 63, No. 11, Article ID 111505, 30 p. (2022). MSC: 35L15 35L71 35B44 35L05 35Q75 PDFBibTeX XMLCite \textit{A. Palmieri} and \textit{H. Takamura}, J. Math. Phys. 63, No. 11, Article ID 111505, 30 p. (2022; Zbl 1508.35022) Full Text: DOI arXiv
Hendy, Ahmed S.; Taha, T. R.; Suragan, D.; Zaky, Mahmoud A. An energy-preserving computational approach for the semilinear space fractional damped Klein-Gordon equation with a generalized scalar potential. (English) Zbl 1503.65229 Appl. Math. Modelling 108, 512-530 (2022). MSC: 65M60 35R11 PDFBibTeX XMLCite \textit{A. S. Hendy} et al., Appl. Math. Modelling 108, 512--530 (2022; Zbl 1503.65229) Full Text: DOI
Palmieri, Alessandro; Takamura, Hiroyuki A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes. (English) Zbl 1498.35361 J. Math. Anal. Appl. 514, No. 1, Article ID 126266, 40 p. (2022). Reviewer: Michael Reissig (Freiberg) MSC: 35L71 35B44 35L15 PDFBibTeX XMLCite \textit{A. Palmieri} and \textit{H. Takamura}, J. Math. Anal. Appl. 514, No. 1, Article ID 126266, 40 p. (2022; Zbl 1498.35361) Full Text: DOI arXiv
Tsutaya, Kimitoshi; Wakasugi, Yuta Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime. (English) Zbl 1479.35864 SN Partial Differ. Equ. Appl. 3, No. 1, Paper No. 6, 10 p. (2022). MSC: 35Q85 35L05 35L70 PDFBibTeX XMLCite \textit{K. Tsutaya} and \textit{Y. Wakasugi}, SN Partial Differ. Equ. Appl. 3, No. 1, Paper No. 6, 10 p. (2022; Zbl 1479.35864) Full Text: DOI arXiv
Nakamura, Makoto The Cauchy problem for the Klein-Gordon equation under the quartic potential in the De Sitter spacetime. (English) Zbl 1492.35242 J. Math. Phys. 62, No. 12, Article ID 121509, 21 p. (2021). MSC: 35Q40 81T20 81R40 83F05 35A01 35A02 PDFBibTeX XMLCite \textit{M. Nakamura}, J. Math. Phys. 62, No. 12, Article ID 121509, 21 p. (2021; Zbl 1492.35242) Full Text: DOI arXiv
Palmieri, Alessandro Semilinear wave equation on compact Lie groups. (English) Zbl 1472.35067 J. Pseudo-Differ. Oper. Appl. 12, No. 3, Paper No. 43, 13 p. (2021). MSC: 35B44 35L15 35L71 35R03 43A30 43A77 58J45 PDFBibTeX XMLCite \textit{A. Palmieri}, J. Pseudo-Differ. Oper. Appl. 12, No. 3, Paper No. 43, 13 p. (2021; Zbl 1472.35067) Full Text: DOI arXiv
Yagdjian, Karen A novel integral transform approach to solving hyperbolic equations in the curved space-times. (English) Zbl 1469.35006 Giga, Yoshikazu (ed.) et al., The role of metrics in the theory of partial differential equations. Proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI), Nagoya University, Japan, July 2–13 2018. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 85, 513-523 (2021). MSC: 35A22 35C15 35L35 35Q05 35Q40 35Q75 PDFBibTeX XMLCite \textit{K. Yagdjian}, Adv. Stud. Pure Math. 85, 513--523 (2021; Zbl 1469.35006) Full Text: DOI
Nakamura, Makoto On the Cauchy problem for the semilinear Proca equations in the de Sitter spacetime. (English) Zbl 1451.35206 J. Differ. Equations 270, 1218-1257 (2021). MSC: 35Q61 35Q60 35Q75 83C22 83F05 PDFBibTeX XMLCite \textit{M. Nakamura}, J. Differ. Equations 270, 1218--1257 (2021; Zbl 1451.35206) Full Text: DOI
Galstian, Anahit; Yagdjian, Karen The global existence of small self-interacting scalar field propagating in the contracting universe. (English) Zbl 1436.35299 NoDEA, Nonlinear Differ. Equ. Appl. 27, No. 3, Paper No. 28, 24 p. (2020). MSC: 35Q85 35L71 35Q40 35Q75 83F05 PDFBibTeX XMLCite \textit{A. Galstian} and \textit{K. Yagdjian}, NoDEA, Nonlinear Differ. Equ. Appl. 27, No. 3, Paper No. 28, 24 p. (2020; Zbl 1436.35299) Full Text: DOI arXiv
Li, Hengyan; Li, Xintao; Yan, Weiping Lifespan of solutions to semilinear damping wave equations in De Sitter spacetime. (English) Zbl 1437.35501 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 195, Article ID 111735, 15 p. (2020). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35L71 35B44 74H35 35L15 PDFBibTeX XMLCite \textit{H. Li} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 195, Article ID 111735, 15 p. (2020; Zbl 1437.35501) Full Text: DOI
Balogh, Andras; Banda, Jacob; Yagdjian, Karen High-performance implementation of a Runge-Kutta finite-difference scheme for the Higgs boson equation in the de Sitter spacetime. (English) Zbl 1508.65084 Commun. Nonlinear Sci. Numer. Simul. 68, 15-30 (2019). MSC: 65L06 83C27 PDFBibTeX XMLCite \textit{A. Balogh} et al., Commun. Nonlinear Sci. Numer. Simul. 68, 15--30 (2019; Zbl 1508.65084) Full Text: DOI arXiv
Tsuchiya, Takuya; Nakamura, Makoto On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the De Sitter spacetime. (English) Zbl 1418.65154 J. Comput. Appl. Math. 361, 396-412 (2019). MSC: 65M99 35L70 35Q75 PDFBibTeX XMLCite \textit{T. Tsuchiya} and \textit{M. Nakamura}, J. Comput. Appl. Math. 361, 396--412 (2019; Zbl 1418.65154) Full Text: DOI arXiv
Yagdjian, Karen Global existence of the self-interacting scalar field in the de Sitter universe. (English) Zbl 1414.35214 J. Math. Phys. 60, No. 5, 051503, 29 p. (2019). MSC: 35Q55 35Q41 81T20 81T10 81V22 PDFBibTeX XMLCite \textit{K. Yagdjian}, J. Math. Phys. 60, No. 5, 051503, 29 p. (2019; Zbl 1414.35214) Full Text: DOI arXiv
Yagdjian, Karen; Balogh, Andras The maximum principle and sign changing solutions of the hyperbolic equation with the Higgs potential. (English) Zbl 1406.35077 J. Math. Anal. Appl. 465, No. 1, 403-422 (2018). MSC: 35B50 35L20 PDFBibTeX XMLCite \textit{K. Yagdjian} and \textit{A. Balogh}, J. Math. Anal. Appl. 465, No. 1, 403--422 (2018; Zbl 1406.35077) Full Text: DOI arXiv
Ebert, M. R.; Reissig, M. Regularity theory and global existence of small data solutions to semi-linear de Sitter models with power non-linearity. (English) Zbl 1387.35080 Nonlinear Anal., Real World Appl. 40, 14-54 (2018). MSC: 35B65 35L71 35L15 PDFBibTeX XMLCite \textit{M. R. Ebert} and \textit{M. Reissig}, Nonlinear Anal., Real World Appl. 40, 14--54 (2018; Zbl 1387.35080) Full Text: DOI arXiv
Kong, De-Xing; Wei, Chang-Hua Lifespan of smooth solutions for timelike extremal surface equation in de Sitter spacetime. (English) Zbl 1370.83011 J. Math. Phys. 58, No. 6, 061502, 27 p. (2017). MSC: 83C15 83C57 83C40 53Z05 35L40 35L65 35Q75 PDFBibTeX XMLCite \textit{D.-X. Kong} and \textit{C.-H. Wei}, J. Math. Phys. 58, No. 6, 061502, 27 p. (2017; Zbl 1370.83011) Full Text: DOI arXiv
Wei, Chang-Hua; Lai, Ning-An Global existence of smooth solutions to exponential wave maps in FLRW spacetimes. (English) Zbl 1370.35197 Pac. J. Math. 289, No. 2, 489-509 (2017). MSC: 35L15 35L05 PDFBibTeX XMLCite \textit{C.-H. Wei} and \textit{N.-A. Lai}, Pac. J. Math. 289, No. 2, 489--509 (2017; Zbl 1370.35197) Full Text: DOI
Galstian, Anahit; Yagdjian, Karen Global in time existence of self-interacting scalar field in de Sitter spacetimes. (English) Zbl 1352.83005 Nonlinear Anal., Real World Appl. 34, 110-139 (2017). MSC: 83C15 83C05 53Z05 53C12 35Q75 35L05 PDFBibTeX XMLCite \textit{A. Galstian} and \textit{K. Yagdjian}, Nonlinear Anal., Real World Appl. 34, 110--139 (2017; Zbl 1352.83005) Full Text: DOI arXiv
Yagdjian, Karen Integral transform approach to time-dependent partial differential equations. (English) Zbl 1391.35013 Qian, Tao (ed.) et al., Mathematical analysis, probability and applications – plenary lectures. ISAAC congress, August 3–8, 2015, Macau, China. Cham: Springer (ISBN 978-3-319-41943-5/hbk; 978-3-319-41945-9/ebook). Springer Proceedings in Mathematics & Statistics 177, 281-336 (2016). MSC: 35A22 35C15 35Q75 35Q05 83F05 76H05 83C57 PDFBibTeX XMLCite \textit{K. Yagdjian}, Springer Proc. Math. Stat. 177, 281--336 (2016; Zbl 1391.35013) Full Text: DOI
Hintz, Peter Global analysis of quasilinear wave equations on asymptotically de Sitter spaces. (Analyse globale des équations d’ondes quasilinéaires sur les espaces asymptotiquement de Sitter.) (English. French summary) Zbl 1456.35141 Ann. Inst. Fourier 66, No. 4, 1285-1408 (2016). MSC: 35L72 35B40 35S05 58J47 35A27 PDFBibTeX XMLCite \textit{P. Hintz}, Ann. Inst. Fourier 66, No. 4, 1285--1408 (2016; Zbl 1456.35141) Full Text: DOI arXiv
Korpusov, M. O.; Mikhailenko, S. G. Blowup of the solution to the Cauchy problem with arbitrary positive energy for a system of Klein-Gordon equations in the de Sitter metric. (English. Russian original) Zbl 1356.35059 Comput. Math. Math. Phys. 56, No. 10, 1758-1762 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 10, 1775-1779 (2016). MSC: 35B44 35L71 35L15 PDFBibTeX XMLCite \textit{M. O. Korpusov} and \textit{S. G. Mikhailenko}, Comput. Math. Math. Phys. 56, No. 10, 1758--1762 (2016; Zbl 1356.35059); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 10, 1775--1779 (2016) Full Text: DOI
Bachelot, Alain On the Klein-Gordon equation near a de Sitter brane. (English. French summary) Zbl 1336.35241 J. Math. Pures Appl. (9) 105, No. 2, 165-197 (2016). MSC: 35L71 35Q85 83E15 35B40 PDFBibTeX XMLCite \textit{A. Bachelot}, J. Math. Pures Appl. (9) 105, No. 2, 165--197 (2016; Zbl 1336.35241) Full Text: DOI arXiv
Yagdjian, Karen Integral transform approach to solving Klein-Gordon equation with variable coefficients. (English) Zbl 1332.35071 Math. Nachr. 288, No. 17-18, 2129-2152 (2015). MSC: 35C15 83F05 35L15 35A22 PDFBibTeX XMLCite \textit{K. Yagdjian}, Math. Nachr. 288, No. 17--18, 2129--2152 (2015; Zbl 1332.35071) Full Text: DOI arXiv
Nakamura, Makoto The Cauchy problem for semi-linear Klein-Gordon equations in de Sitter spacetime. (English) Zbl 1312.35125 J. Math. Anal. Appl. 410, No. 1, 445-454 (2014). MSC: 35L15 35Q75 35L71 PDFBibTeX XMLCite \textit{M. Nakamura}, J. Math. Anal. Appl. 410, No. 1, 445--454 (2014; Zbl 1312.35125) Full Text: DOI
Yagdjian, Karen Huygens’ principle for the Klein-Gordon equation in the de Sitter spacetime. (English) Zbl 1284.81125 J. Math. Phys. 54, No. 9, 091503, 18 p. (2013). MSC: 81Q05 81Q35 PDFBibTeX XMLCite \textit{K. Yagdjian}, J. Math. Phys. 54, No. 9, 091503, 18 p. (2013; Zbl 1284.81125) Full Text: DOI arXiv
Yagdjian, Karen Global solutions of semilinear system of Klein-Gordon equations in de Sitter spacetime. (English) Zbl 1278.35149 Reissig, Michael (ed.) et al., Progress in partial differential equations. Asymptotic profiles, regularity and well-posedness. Based on the presentations given at a session at the 8th ISAAC congress, Moscow, Russia, August 22–27, 2011. Cham: Springer (ISBN 978-3-319-00124-1/hbk; 978-3-319-00125-8/ebook). Springer Proceedings in Mathematics & Statistics 44, 409-444 (2013). Reviewer: Chengbo Wang (Hangzhou) MSC: 35L52 35L71 81T20 35C15 PDFBibTeX XMLCite \textit{K. Yagdjian}, Springer Proc. Math. Stat. 44, 409--444 (2013; Zbl 1278.35149) Full Text: DOI
Baskin, Dean Strichartz estimates on asymptotically de Sitter spaces. (English) Zbl 1262.83020 Ann. Henri Poincaré 14, No. 2, 221-252 (2013). MSC: 83C30 83C05 83C15 35L05 83C25 PDFBibTeX XMLCite \textit{D. Baskin}, Ann. Henri Poincaré 14, No. 2, 221--252 (2013; Zbl 1262.83020) Full Text: DOI arXiv
Yagdjian, Karen Global existence of the scalar field in de Sitter spacetime. (English) Zbl 1252.83020 J. Math. Anal. Appl. 396, No. 1, 323-344 (2012). MSC: 83C05 53Z05 83C15 35L05 83C25 83A05 83C40 PDFBibTeX XMLCite \textit{K. Yagdjian}, J. Math. Anal. Appl. 396, No. 1, 323--344 (2012; Zbl 1252.83020) Full Text: DOI
Yagdjian, Karen On the global solutions of the Higgs boson equation. (English) Zbl 1242.35203 Commun. Partial Differ. Equations 37, No. 1-3, 447-478 (2012). MSC: 35Q75 35L71 35B05 35B40 35D30 PDFBibTeX XMLCite \textit{K. Yagdjian}, Commun. Partial Differ. Equations 37, No. 1--3, 447--478 (2012; Zbl 1242.35203) Full Text: DOI arXiv