Remarks on Blow-Up Phenomena in $p$-Laplacian Heat Equation with Inhomogeneous Nonlinearity

Authors

Eadah Ahmad Alzahrani Deapartment of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam, Saudi Arabia & Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia.
Mohamed Majdoub Deapartment of Mathematics, College of Science, Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam, Saudi Arabia & Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, 31441, Dammam, Saudi Arabia.

DOI:

https://doi.org/10.4208/jpde.v34.n1.3

Keywords:

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

Abstract

We investigate the $p$-Laplace heat equation $u_t-\\Delta_p u=\u03b6(t)f(u)$ in a bounded smooth domain. Using differential-inequality arguments, we prove blow-up results under suitable conditions on $\u03b6,$ $f,$ and the initial datum $u_0$. We also give an upper bound for the blow-up time in each case.<\/p>"

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Published

2021-05-28

Issue

Vol. 34 No. 1 (2021)

Section

Articles