References
- Zhang ZC, Li Y. Blowup and existence of global solutions to nonlinear parabolic equations with degenerate diffusion. Electron J Differ Equ. 2013;2013:1–17.
- Zhang ZC, Li Y. Classification of blowup solutions for a parabolic p-Laplacian equation with nonlinear gradient terms. J Math Anal Appl. 2016;436:1266–1283.
- Lu HQ, Zhang ZC. Blowup time estimates for a parabolic p-Laplacian equation with nonlinear gradient terms. Z Angew Math Phys. 2019;70:1–18.
- Li Y, Zhang ZC, Zhu LP. Classification of certain qualitative properties of solutions for the quasilinear parabolic equations. Sci China Math. 2018;61:855–868.
- Zhao JN, Liang ZL. Blow-up rate of solutions for p-Laplacian equation. J Partial Differ Equ. 2008;21:134–140.
- Galaktionov VA, Posashkov SA. Single point blow-up for N-dimensional quasilinear equations with gradient diffusion and source. Indiana Univ Math J. 1991;40:1041–1060.
- Zhang ZC. Gradient blowup rate for a viscous Hamilton–Jacobi equation with degenerate diffusion. Arch Math. 2013;100:361–367.
- Guo JS, Hu B. Blowup rate estimates for the heat equation with a nonlinear gradient source term. Discrete Contin Dyn Syst. 2008;20:927–937.
- Li YX, Xie CH. Blow-up for p-Laplacian parabolic equations. Electron J Differ Equ. 2003;2003:1–12.
- Li YX, Souplet P.. Single-point gradient blow-up on the boundary for diffusive Hamilton–Jacobi equation with gradient domains. Commun Math Phys. 2003;293:499–517.
- Quittner P, Souplet P.. Superlinear parabolic problems: blow-up, global existence and steady states. Basel: Birkhäuser; 2007.
- Zhang ZC, Hu B. Gradient blowup rate for a semilinear parabolic equation. Discrete Contin Dyn Syst. 2010;26:767–779.
- Zhao JN. Existence and nonexistence of solutions for ut=div(|∇u|p−2)+f(∇u,u,x,t). J Math Anal Appl. 1993;172:130–146.
- Antontsev SN, Chipot M, Shmarev SI. Uniqueness and comparison theorems for solutions of doubly nonlinear parabolic equations with nonstandard growth conditions. Commun Pure Appl Anal. 2013;12:1527–1546.
- Guo B, Li YJ, Gao WJ. Singular phenomena of solutions for nonlinear diffusion equations involving p(x)-Laplace operator and nonlinear source. Z Angew Math Phys. 2015;66:989–1005.
- Liu BC, Dong MZ. A nonlinear diffusion problem with convection and anisotropic nonstandard growth conditions. Nonlinear Anal Real World Appl. 2019;48:383–409.
- Liu BC, Dong MZ, Li FJ. Singular solutions in nonlinear parabolic equations with anisotropic nonstandard growth conditions. J Math Phys. 2018;59:121504.
- Ladyzhenskaya OA, Solonnikow VA, Ural'ceva NN. Linear and quasi-Linear equations of parabolic type. Rhode Island: American Mathematical Society; 1968.
- DiBenedetto E. Degenerate parabolic equations. New York: Springer-Verlag; 1993.
- DiBenedetto E, Friedman A. Hölder estimates for nonlinear degenerate parabolic systems. J Fur Reine Angew Math. 1985;357:1–22.
- Attouchi A. Well-posedness and gradient blow-up estimate near the boundary for a Hamilton–Jacobi equation with degenerate diffusion. J Differ Equ. 2012;253:2474–2492.
- Bartier. Ph. Laurencot JP. Gradient estimates for a degenerate parabolic equation with gradient absorption and applications. J Funct Anal. 2008;254:851–878.
- Souplet P., Zhang Q. Global solutions of inhomogeneous Hamilton–Jacobi equations. J Anal Math. 2006;99:355–396.
- Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 2001.