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Blow-up solutions of damped Klein–Gordon equation on the Heisenberg group

Michael Ruzhansky (UGent) and Bolys Sabitbek
(2023) EUROPEAN JOURNAL OF MATHEMATICS. 9(3).
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Abstract
We prove the blow-up of solutions of the semilinear damped Klein-Gordon equation in a finite time for arbitrary positive initial energy on the Heisenberg group. This work complements the paper Ruzhansky and Tokmagambetov (J Differ Equ 265(10):5212-5236, 2018), where the global in time well-posedness was proved for the small energy solutions.
Keywords
General Mathematics, Ghent Analysis & PDE center, Blow-up, Sub-Laplacian, Heisenberg group, Damped Klein-Gordon equation, GLOBAL-SOLUTIONS, WAVE-EQUATION, NONEXISTENCE THEOREMS, INSTABILITY, EXPONENT, SPACES

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MLA
Ruzhansky, Michael, and Bolys Sabitbek. “Blow-up Solutions of Damped Klein–Gordon Equation on the Heisenberg Group.” EUROPEAN JOURNAL OF MATHEMATICS, vol. 9, no. 3, 2023, doi:10.1007/s40879-023-00654-9.
APA
Ruzhansky, M., & Sabitbek, B. (2023). Blow-up solutions of damped Klein–Gordon equation on the Heisenberg group. EUROPEAN JOURNAL OF MATHEMATICS, 9(3). https://doi.org/10.1007/s40879-023-00654-9
Chicago author-date
Ruzhansky, Michael, and Bolys Sabitbek. 2023. “Blow-up Solutions of Damped Klein–Gordon Equation on the Heisenberg Group.” EUROPEAN JOURNAL OF MATHEMATICS 9 (3). https://doi.org/10.1007/s40879-023-00654-9.
Chicago author-date (all authors)
Ruzhansky, Michael, and Bolys Sabitbek. 2023. “Blow-up Solutions of Damped Klein–Gordon Equation on the Heisenberg Group.” EUROPEAN JOURNAL OF MATHEMATICS 9 (3). doi:10.1007/s40879-023-00654-9.
Vancouver
1.
Ruzhansky M, Sabitbek B. Blow-up solutions of damped Klein–Gordon equation on the Heisenberg group. EUROPEAN JOURNAL OF MATHEMATICS. 2023;9(3).
IEEE
[1]
M. Ruzhansky and B. Sabitbek, “Blow-up solutions of damped Klein–Gordon equation on the Heisenberg group,” EUROPEAN JOURNAL OF MATHEMATICS, vol. 9, no. 3, 2023.
@article{01HP4QVKJ5815Y884SFTG58Z9V,
  abstract     = {{We prove the blow-up of solutions of the semilinear damped Klein-Gordon equation in a finite time for arbitrary positive initial energy on the Heisenberg group. This work complements the paper Ruzhansky and Tokmagambetov (J Differ Equ 265(10):5212-5236, 2018), where the global in time well-posedness was proved for the small energy solutions.}},
  articleno    = {{61}},
  author       = {{Ruzhansky, Michael and Sabitbek, Bolys}},
  issn         = {{2199-675X}},
  journal      = {{EUROPEAN JOURNAL OF MATHEMATICS}},
  keywords     = {{General Mathematics,Ghent Analysis & PDE center,Blow-up,Sub-Laplacian,Heisenberg group,Damped Klein-Gordon equation,GLOBAL-SOLUTIONS,WAVE-EQUATION,NONEXISTENCE THEOREMS,INSTABILITY,EXPONENT,SPACES}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{12}},
  title        = {{Blow-up solutions of damped Klein–Gordon equation on the Heisenberg group}},
  url          = {{http://doi.org/10.1007/s40879-023-00654-9}},
  volume       = {{9}},
  year         = {{2023}},
}
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