The prior estimate and decay property of positive solutions are derived for a system of quasi-linear elliptic differential equations first. Hence, the result of non-existence for differential equation system of radially nonincreasing positive solutions is implied. By using this non-existence result, blow-up estimates for a class quasi-linear reaction-diffusion systems (non-Newtonian filtration systems) are established, which extends the result of semi-linear reaction-diffusion (Fujita type) systems.
blow-up blow-up rates quasi-linear equation system
This is a preview of subscription content, log in to check access.
Gabriella C, Mitidieri E. Blow-up estimates of positive solutions of a parabolic system[J].J Differential Equations, 1994,113(2):265–271.MathSciNetCrossRefGoogle Scholar
Mitidieri E. Nonexistence of positive solutions of semi-linear elliptic system inRN[J].Differential Integral Equations, 1996,9(3):465–479.zbMATHMathSciNetGoogle Scholar
Escobedo M, Levine A H. Critical blow-up and global existence numbers for a weakly coupled system of reaction-diffusion equations[J].Arch Rational Mech Anal, 1995,129(1):47–100.zbMATHMathSciNetCrossRefGoogle Scholar
WU Z Q, Yuan H J. Uniqueness of generalized solutions for a quasi-linear degenerate parabolic system[J].J Partial Differential Equations, 1995,8(1):89–96.zbMATHMathSciNetGoogle Scholar
Mitidieri E, Sweers G, Vorst Vander R. Nonexistence theorems for systems of quasi-linear partial differential equations[J].Differential Integral Equations, 1995,8(6):1331–1354.zbMATHMathSciNetGoogle Scholar
Clement Ph, Manasevich R, Mitidieri E. Positive solutions for a quasi-linear system via blow up [J].Comm in Partial Differential Equations, 1993,18(12):2071–2106.zbMATHMathSciNetGoogle Scholar
GUO Zong-ming. Existence of positive radial solutions for certain quasi-linear elliptic systems[J].Chinese Ann Math, 1996,17A(3):573–582.Google Scholar