L ∞ estimates of solutions for the quasilinear parabolic equation with nonlinear gradient term and L 1 data

Abstract

In this article, we study the quasilinear parabolic problem (Equation presented) where Ω is a bounded domain in ℝ N, m > 0 and g(u) satisfies |g(u)| ≤ K 1|u| 1+V with 0 ≤ v 1, 0 ≤ p max{m + 2, q + β}. © 2012 Chen et al; licensee Springer.