References
- Ei SI. The effect of nonlocal convection on reaction-diffusion equations. Hiroshima Math. J. 1987;7:281–307.
- Nagai T, Mimura M. Asymptotic behavior for a nonlinear degenerate diffusion equation in population dynamics. SIAM J. Appl. Math. 1983;43:449–464.
- Quittner P, Souplet P. Superlinear parabolic problems. Blow-up, global existence and steady states. Basel: Birkhäuser Verlag; 2007.
- Fujita H. On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α. J. Faculty Sci. Univ. Tokyo Sect. IA Math. 1966;13:109–124.
- Deng K, Levine HA. The role of critical exponents in blow-up theorems: the sequel. J. Math. Anal. Appl. 2000;243:85–126.
- Levine HA. The role of critical exponents in blowup theorems. SIAM Rev. 1990;32:262–288.
- Galaktionov VA, Kurdyumov SP, Mikhailov AP, et al. Unbounded solutions of the Cauchy problem for the parabolic equation ut=∇(uα ∇ u)+uβ. Sov. Phys. Dokl. 1980;25:458–459.
- Andreucci D, DiBenedetto E. On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources. Ann. Scuola Normale Superiore Pisa Cl. Sci. Ser. 4. 1991;18:393–441.
- Andreucci D. Degenerate parabolic equations with initial data measures. Trans. Am. Math. Soc. 1997;349:3911–3923.
- Ben-Artzi M, Souplet P, Weissler FB. The local theory for viscous Hamilton--Jacobi equations in Lebesgue spaces. J. Math. Pures Appl. 2002;81:343–378.
- Shang HF. Cauchy problem for nonlinear parabolic equations with a gradient term. J. Differ. Equ. 2014;257:2801–2825.
- Chadam JM, Peirce A, Yin HM. The blowup property of solutions to some diffusion equations with localized nonlinear reactions. J. Math. Anal. Appl. 1992;169:313–328.
- Deng K, Kwong MK, Levine HA. The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers’ equation. Q. Appl. Math. 1992;50:173–200.
- Rouchon P. Universal bounds for global solutions of a diffusion equation with a nonlocal reaction term. J. Differ. Equ. 2003;193:75–94.
- Souplet P. Blow-up in nonlocal reaction-diffusion equations. SIAM J. Math. Anal. 1998;29:1301–1334.
- Souplet P. Uniform blow-up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source. J. Differ. Equ. 1999;153:374–406.
- Anderson JR, Deng K. Global existence for degenerate parabolic equations with a non-local forcing. Math. Methods Appl. Sci. 1997;20:1069–1087.
- Du LL, Yao ZA. Localization of blow-up points for a nonlinear nonlocal porous medium equation. Commun. Pure Appl. Anal. 2007;6:183–190.
- Li FC, Xie CH. Global existence and blow-up for a nonlinear porous medium equation. Appl. Math. Lett. 2003;16:185–192.
- Liu DM, Mu CL, Xin Q. Lower bounds estimate for the blow-up time of a nonlinear nonlocal porous medium equation, Acta Math. Sci. Ser. B English Ed. 2012;32:1206–1212.
- Galaktionov VA, Levine HA. A general approach to critical Fujita exponents in nonlinear parabolic problems. Nonlinear Anal. 1998;34:1005–1027.
- Afanaseva NV, Tedeev AF. Theorems on the existence and nonexistence of solutions to the Cauchy problem for degenerate parabolic equations with a nonlocal source. Ukrain. Mat. Zh. 2005;57:1443–1464. Russian; translation in Ukrainian Math. J. 2005:57:1687--1711.
- Andreucci D, DiBenedetto E. A new approach to initial traces in nonlinear filtration. Ann. Inst. Henri Poincaré Anal. Non Linéaire. 1990;7:305–334.
- Ladyzhenskaja OA, Solonnikov VA, Ural’ceva NN. Linear and quasilinear equations of parabolic type. Providence (RI): American Mathematical Society; 1968.
- DiBenedetto E. Degenerate parabolic equations. New York (NY): Springer-Verlag; 1993.
- DiBenedetto E, Friedman A. Hölder estimates for nonlinear degenerate parabolic systems. J. Reine Angew. Math. 1985;357:1–22.
- Andreucci D. New results on the Cauchy problem for parabolic systems and equations with strongly nonlinear sources. Manuscripta Math. 1992;77:127–159.