Remarks on Blow-Up Phenomena in $p$-Laplacian Heat Equation with Inhomogeneous Nonlinearity (Journal of Partial Differential Equations, 2021)
"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."
Keywords: Parabolic problems; $p$-Laplacian equation; blow-up; positive initial energy.