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Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux. (English) Zbl 1078.35046
Positive solutions of a quasilinear parabolic system on a halfline with a nonlinear boundary condition are studied. Results on global existence and nonexistence, on the blow-up rate and blow-up set are established.

MSC:
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35B33Critical exponents (PDE)
35K55Nonlinear parabolic equations
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References:
[1] Deng, K.; Levine, H. A.: The role of critical exponents in blow-up theorems: the sequel. J. math. Anal. appl. 243, 85-126 (2000) · Zbl 0942.35025
[2] Dibenedetto, E.: Continuity of weak solutions to a general porous medium equation. Indiana univ. Math. J. 32, 83-118 (1983) · Zbl 0526.35042
[3] Escobedo, M.; Levine, H. A.: Critical blow-up and global existence numbers for a weakly coupled system of reaction--diffusion equations. Arch. rational mech. Anal. 129, 47-100 (1995) · Zbl 0822.35068
[4] Galaktionov, V. A.: Blow-up for quasilinear heat equations with critical Fujita’s exponents. Proc. roy. Soc. Edinburgh sect. A 124, 517-525 (1994) · Zbl 0808.35053
[5] Galaktionov, V. A.; Levine, H. A.: On critical Fujita exponents for heat equations with nonlinear flux boundary conditions on the boundary. Israel J. Math. 94, 125-146 (1996) · Zbl 0851.35067
[6] Giga, Y.; Kohn, R. V.: Asymptotically self-similar blow-up of semilinear heat equations. Comm. pure appl. Math. 38, 297-319 (1985) · Zbl 0585.35051
[7] Gilding, B. H.; Herrero, M. A.: Localization and blow-up of thermal waves in nonlinear heat conduction with peaking. Math. ann. 282, 223-242 (1988) · Zbl 0627.35048
[8] Hu, B.; Yin, H. M.: The profile near blow-up time for the solution of the heat equation with a nonlinear boundary condition. Trans. amer. Math. soc. 346, 117-135 (1994) · Zbl 0823.35020
[9] Kalashinikov, A. S.: Some problems of qualitative theory of nonlinear degenerate parabolic equations of second order. Usp. mat. Nauk 42, 135-176 (1987)
[10] Levine, H. A.: The role of critical exponents in blow up theorems. SIAM rev. 32, 262-288 (1990) · Zbl 0706.35008
[11] Lieberman, G. M.: Hölder continuity of gradient of solutions of uniformly parabolic equations with conormal boundary conditions. Ann. math. Pura appl. 148, 77-99 (1987) · Zbl 0658.35050
[12] Lieberman, G. M.: Second order parabolic differential equations. (1996) · Zbl 0884.35001
[13] Pao, C. V.: Nonlinear parabolic and elliptic equations. (1992) · Zbl 0777.35001
[14] Quirós, F.; Rossi, J. D.: Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions. Indiana univ. Math. J. 50, 629-654 (2001) · Zbl 0994.35027
[15] Rossi, J. D.; Wolanski, N.: Global existence and nonexistence for a parabolic system with nonlinear boundary conditions. Differential integral equations 11, 179-190 (1998) · Zbl 1004.35012
[16] Wang, S.; Xie, C. H.; Wang, M. X.: The blow-up rate for a system of heat equations completely coupled in the boundary conditions. Nonlinear anal. 35, 389-398 (1999) · Zbl 0919.35062
[17] Zheng, S. N.: Nonexistence of positive solutions for a semilinear elliptic system and blow-up estimates for a reaction--diffusion system. J. math. Anal. appl. 232, 293-311 (1999) · Zbl 0935.35042
[18] Zheng, S. N.: Global existence and global non-existence of solutions to a reaction--diffusion system. Nonlinear anal. 39, 327-340 (2000) · Zbl 0955.35039