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Critical exponents for the p-Laplace heat equations with combined nonlinearities

Berikbol Torebek (UGent)
(2023) JOURNAL OF EVOLUTION EQUATIONS. 23(4).
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Abstract
This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of the heat equations with combined nonlinearities considered by Jleli et al. (Proc Am Math Soc 148:2579–2593, 2020). Firstly, we focus on an interesting phenomenon of discontinuity of the critical exponents. In particular, we will fill the gap in the results of Jleli et al. (2020) for the critical case. We are also interested in the influence of the forcing term on the critical behavior of the considered problem, so we will define another critical exponent depending on the forcing term.
Keywords
P-Laplace heat equation, Combined nonlinearities, Critical exponents, Global solutions, CAUCHY-PROBLEM, PARABOLIC EQUATION, GLOBAL EXISTENCE, GRADIENT TERM, BEHAVIOR

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MLA
Torebek, Berikbol. “Critical Exponents for the P-Laplace Heat Equations with Combined Nonlinearities.” JOURNAL OF EVOLUTION EQUATIONS, vol. 23, no. 4, 2023, doi:10.1007/s00028-023-00922-x.
APA
Torebek, B. (2023). Critical exponents for the p-Laplace heat equations with combined nonlinearities. JOURNAL OF EVOLUTION EQUATIONS, 23(4). https://doi.org/10.1007/s00028-023-00922-x
Chicago author-date
Torebek, Berikbol. 2023. “Critical Exponents for the P-Laplace Heat Equations with Combined Nonlinearities.” JOURNAL OF EVOLUTION EQUATIONS 23 (4). https://doi.org/10.1007/s00028-023-00922-x.
Chicago author-date (all authors)
Torebek, Berikbol. 2023. “Critical Exponents for the P-Laplace Heat Equations with Combined Nonlinearities.” JOURNAL OF EVOLUTION EQUATIONS 23 (4). doi:10.1007/s00028-023-00922-x.
Vancouver
1.
Torebek B. Critical exponents for the p-Laplace heat equations with combined nonlinearities. JOURNAL OF EVOLUTION EQUATIONS. 2023;23(4).
IEEE
[1]
B. Torebek, “Critical exponents for the p-Laplace heat equations with combined nonlinearities,” JOURNAL OF EVOLUTION EQUATIONS, vol. 23, no. 4, 2023.
@article{01J066HBWHMZFJ4QWMX0WSJCH5,
  abstract     = {{This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of the heat equations with combined nonlinearities considered by Jleli et al. (Proc Am Math Soc 148:2579–2593, 2020). Firstly, we focus on an interesting phenomenon of discontinuity of the critical exponents. In particular, we will fill the gap in the results of Jleli et al. (2020) for the critical case. We are also interested in the influence of the forcing term on the critical behavior of the considered problem, so we will define another critical exponent depending on the forcing term.}},
  articleno    = {{71}},
  author       = {{Torebek, Berikbol}},
  issn         = {{1424-3199}},
  journal      = {{JOURNAL OF EVOLUTION EQUATIONS}},
  keywords     = {{P-Laplace heat equation,Combined nonlinearities,Critical exponents,Global solutions,CAUCHY-PROBLEM,PARABOLIC EQUATION,GLOBAL EXISTENCE,GRADIENT TERM,BEHAVIOR}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{15}},
  title        = {{Critical exponents for the p-Laplace heat equations with combined nonlinearities}},
  url          = {{http://doi.org/10.1007/s00028-023-00922-x}},
  volume       = {{23}},
  year         = {{2023}},
}
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