... the main ideas. The main results in this article were derived byCC. FY and ZY participated in the discussion of topic. All authors read and approved the finalmanuscript.Acknowledgments The authors ... distribution, and reproduction in any medium, provided the original work is properly cited.L∞estimates of solutions for the quasilinear parabolicequation with nonlinear gradient term and L1dataCaisheng ... parabolic problems with L1data. Nonlinear Anal. 28, 1943–1954 (1997)[12] Ladyzenskaya, OA, Solonnikov, VA, Uraltseva, NN: Linear and Quasilinear Equations of Parabolic Type. AMS, Providence (1969)[13]...