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Fujita-type results for the degenerate parabolic equations on the Heisenberg groups

Ahmad Z. Fino, Michael Ruzhansky (UGent) and Berikbol Torebek (UGent)
(2024) NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. 31(2).
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Abstract
In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponents, which depend on the homogeneous dimension of the Heisenberg groups. The analysis includes the case of porous medium equations. Our proof approach is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg groups. We also use the Kaplan eigenfunctions method in combination with the Hopf-type lemma on the Heisenberg groups.
Keywords
Applied Mathematics, Analysis, Ghent Analysis & PDE center, Porous medium equation, Degenerate parabolic equation, Critical exponents, Heisenberg group, POROUS-MEDIUM EQUATION, BLOW-UP, CRITICAL EXPONENT, GLOBAL EXISTENCE, INEQUALITIES, NONEXISTENCE

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Citation

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MLA
Fino, Ahmad Z., et al. “Fujita-Type Results for the Degenerate Parabolic Equations on the Heisenberg Groups.” NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, vol. 31, no. 2, 2024, doi:10.1007/s00030-023-00907-2.
APA
Fino, A. Z., Ruzhansky, M., & Torebek, B. (2024). Fujita-type results for the degenerate parabolic equations on the Heisenberg groups. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 31(2). https://doi.org/10.1007/s00030-023-00907-2
Chicago author-date
Fino, Ahmad Z., Michael Ruzhansky, and Berikbol Torebek. 2024. “Fujita-Type Results for the Degenerate Parabolic Equations on the Heisenberg Groups.” NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS 31 (2). https://doi.org/10.1007/s00030-023-00907-2.
Chicago author-date (all authors)
Fino, Ahmad Z., Michael Ruzhansky, and Berikbol Torebek. 2024. “Fujita-Type Results for the Degenerate Parabolic Equations on the Heisenberg Groups.” NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS 31 (2). doi:10.1007/s00030-023-00907-2.
Vancouver
1.
Fino AZ, Ruzhansky M, Torebek B. Fujita-type results for the degenerate parabolic equations on the Heisenberg groups. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. 2024;31(2).
IEEE
[1]
A. Z. Fino, M. Ruzhansky, and B. Torebek, “Fujita-type results for the degenerate parabolic equations on the Heisenberg groups,” NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, vol. 31, no. 2, 2024.
@article{01HNZNVFM4A35MA8H6GVM2YBGD,
  abstract     = {{In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponents, which depend on the homogeneous dimension of the Heisenberg groups. The analysis includes the case of porous medium equations. Our proof approach is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg groups. We also use the Kaplan eigenfunctions method in combination with the Hopf-type lemma on the Heisenberg groups.}},
  articleno    = {{19}},
  author       = {{Fino, Ahmad Z. and Ruzhansky, Michael and Torebek, Berikbol}},
  issn         = {{1021-9722}},
  journal      = {{NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS}},
  keywords     = {{Applied Mathematics,Analysis,Ghent Analysis & PDE center,Porous medium equation,Degenerate parabolic equation,Critical exponents,Heisenberg group,POROUS-MEDIUM EQUATION,BLOW-UP,CRITICAL EXPONENT,GLOBAL EXISTENCE,INEQUALITIES,NONEXISTENCE}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{37}},
  title        = {{Fujita-type results for the degenerate parabolic equations on the Heisenberg groups}},
  url          = {{http://doi.org/10.1007/s00030-023-00907-2}},
  volume       = {{31}},
  year         = {{2024}},
}
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