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 - <p style="text-align: justify;">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.</p>