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Volume 34, Issue 1
Remarks on Blow-Up Phenomena in $p$-Laplacian Heat Equation with Inhomogeneous Nonlinearity

Eadah Ahmad Alzahrani & Mohamed Majdoub

DOI: 10.4208/jpde.v34.n1.3

J. Part. Diff. Eq., 34 (2021), pp. 42-50.

Published online: 2021-01

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  • Abstract

We investigate the $p$-Laplace heat equation $u_t-\Delta_p u=ζ(t)f(u)$ in a bounded smooth domain. Using differential-inequality arguments, we prove blow-up results under suitable conditions on $ζ,$ $f,$ and the initial datum $u_0$. We also give an upper bound for the blow-up time in each case.

  • Keywords

Parabolic problems, $p$-Laplacian equation, blow-up, positive initial energy.

  • AMS Subject Headings

35K55, 35K65, 35K61, 35B30, 35B44

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ealzahrani@iau.edu.sa (Eadah Ahmad Alzahrani)

mmajdoub@iau.edu.sa (Mohamed Majdoub)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-42, author = {Alzahrani , Eadah Ahmad and Majdoub , Mohamed}, title = {Remarks on Blow-Up Phenomena in $p$-Laplacian Heat Equation with Inhomogeneous Nonlinearity}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {1}, pages = {42--50}, abstract = {

We investigate the $p$-Laplace heat equation $u_t-\Delta_p u=ζ(t)f(u)$ in a bounded smooth domain. Using differential-inequality arguments, we prove blow-up results under suitable conditions on $ζ,$ $f,$ and the initial datum $u_0$. We also give an upper bound for the blow-up time in each case.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/18553.html} }
TY - JOUR T1 - Remarks on Blow-Up Phenomena in $p$-Laplacian Heat Equation with Inhomogeneous Nonlinearity AU - Alzahrani , Eadah Ahmad AU - Majdoub , Mohamed JO - Journal of Partial Differential Equations VL - 1 SP - 42 EP - 50 PY - 2021 DA - 2021/01 SN - 34 DO - http://doi.org/10.4208/jpde.v34.n1.3 UR - https://global-sci.org/intro/article_detail/jpde/18553.html KW - Parabolic problems, $p$-Laplacian equation, blow-up, positive initial energy. AB -

We investigate the $p$-Laplace heat equation $u_t-\Delta_p u=ζ(t)f(u)$ in a bounded smooth domain. Using differential-inequality arguments, we prove blow-up results under suitable conditions on $ζ,$ $f,$ and the initial datum $u_0$. We also give an upper bound for the blow-up time in each case.

Alzahrani , Eadah Ahmad and Majdoub , Mohamed. (2021). Remarks on Blow-Up Phenomena in $p$-Laplacian Heat Equation with Inhomogeneous Nonlinearity. Journal of Partial Differential Equations. 34 (1). 42-50. doi:10.4208/jpde.v34.n1.3
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