References
- Friedman A. Partial differential equations of parabolic type. Upper Saddle River: Prentice Hall; 1964.
- Dibenedetto E. Degenerate parabolic equations. New York (NY): Springer; 1993.
- Levine HA, Payne LE. Nonexistence theorems for the heat equation with nonlinear boundary conditions and for porous medium equation backward in time. J Differ Equ. 1974;16:319–334.
- Filo J. Diffusivity versus absorption through the boundary. J Differ Equ. 1992;99:281–305.
- Kalashnikov AS. Some problems of the qualitative theory of second-order nonlinear degenerate parabolic equations. Usp Mat Nauk. 1987;42:135–176.
- Deng K, Levine HA. The role of critical exponents in blow-up theorems: the sequel. J Math Anal Appl. 2000;243:85–126.
- Galaktionov VA, Vazquez JL. The problem of blow-up in nonlinear parabolic equations. Discrete Contin Dyn Syst. 2002;8:399–433.
- Pao CV. Nonlinear parabolic and elliptic equation. New York (NY): Plenum; 1992.
- Samarskii AA, Galaktionov VA, Kurdyumov SP, et al. Blow-up in quasilinear parabolic equations. Berlin: Walter de Gruyter; 1995.
- Wu ZQ, Zhao JN, Yin JX, et al. Nonlinear diffusion equations. River Edge: World Scientific; 2001.
- Fujita H. On the blowing up of solution of the Cauchy problem for ut=Δu+u1+α. J Fac Sci Univ Tokyo Sect I. 1966;13:109–124.
- Galaktionov VA. Conditions for nonexistence as a whole and localization of the solutions of Cauchy's problem for a class of nonlinear parabolic equations. Zh Vychisl Mat Mat Fiz. 1985;23:1341–1354.
- Qi YW, Wang MX. Critical exponents of quasilinear parabolic equations. J Math Anal Appl. 2002;267:264–280.
- Galaktionov VA, Levine HA. A general approach to critical Fujita exponents in nonlinear parabolic problems. Nonlinear Anal. 1998;34:1005–1027.
- Ma LW, Fang ZB. A new second critical exponent and life span for a quasilinear degenerate parabolic equation with weighted nonlocal sources. Commun Pure Appl Anal. 2017;16:1697–1706.
- Ma LW, Fang ZB. Secondary critical exponent and life span for a nonlocal parabolic p-Laplace equation. Appl Anal. 2018;97:775–786.
- Zheng YD, Fang ZB. New critical exponents, large time behavior, and life span for a fast diffusive p-Laplacian equation with nonlocal source. Z Angew Math Phys. 2019;70:144–00.
- Zheng YD, Fang ZB. New critical exponents for a doubly singular parabolic equation. Appl Anal. doi: https://doi.org/10.1080/00036811.2019.1687885. in press.
- Zheng YD, Fang ZB. Critical exponents for a non-Newtonian polytropic filtration equation with weighted nonlocal inner sources. Math Methods Appl Sci. 2020;43:2403–2420.
- Deng K, Fila M, Levine HA. On critical exponents for a system of heat equations coupled in the boundary conditions. Acta Math Univ Comenian (N.S.). 1994;63:169–192.
- Li ZP, Mu CL. Critical curves for fast diffusive non-Newtonian equations coupled via nonlinear boundary flux. J Math Anal Appl. 2008;340:876–883.
- Li ZP, Du WJ. Global existence and nonexistence for a fast diffusive equation with multiple nonlinearities. Int J Nonlinear Sci. 2011;12:419–426.
- Li ZP, Mu CL, Xie L. Critical curves for a degenerate parabolic equation with multiple nonlinearities. J Math Anal Appl. 2009;359:39–47.
- Liu BC, Zhang Q, Zhang X, et al. Critical curves of solutions in nonlinear parabolic equations involving p,m-Laplace operators. Bull Iranian Math Soc. 2018;44:1427–1447.
- Aripov MM, Raimbekov JR. The critical curves of a doubly nonlinear parabolic equation in non-divergent form with a source and nonlinear boundary flux. Zh Sib Fed Univ Mat Fiz. 2019;12:112–124.