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

Author(s)

    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.
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    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.
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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>"

Keywords:

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

10.4208/jpde.v34.n1.3

How to Cite

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