Initial and boundary blow-up problem for $p$-Laplacian parabolic equation with general absorption

In this article, we investigate the initial and boundary blow-up problem for the $p$-Laplacian parabolic equation $u_t-Δ_p u=-b(x,t)f(u)$ over a smooth bounded domain $Ω$ of $\mathbb{R}^N$ with $N\ge2$, where $Δ_pu={\rm div}(|\nabla u|^{p-2}\nabla u)$ with $p>1$, and $f(u)$ is a function of regular variation at infinity. We study the existence and uniqueness of positive solutions, and their asymptotic behaviors near the parabolic boundary.

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