Fujita type theorems for a class of semilinear parabolic equations with a gradient term
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Authors
Yuanyuan Nie
- School of Mathematics, Jilin University, Changchun 130012, China.
Mingjun Zhou
- School of Mathematics, Jilin University, Changchun 130012, China.
Qian Zhou
- School of Mathematics, Jilin University, Changchun 130012, China.
Yang Na
- School of Mathematics, Jilin University, Changchun 130012, China.
Abstract
This paper concerns the asymptotic behavior of solutions to the Neumann exterior problem of a class of semilinear parabolic
equations with a gradient term. The blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated
by spacial dimension, the behavior of the coefficient of the gradient term at infinity and other exponents.
Share and Cite
ISRP Style
Yuanyuan Nie, Mingjun Zhou, Qian Zhou, Yang Na, Fujita type theorems for a class of semilinear parabolic equations with a gradient term, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1603--1612
AMA Style
Nie Yuanyuan, Zhou Mingjun, Zhou Qian, Na Yang, Fujita type theorems for a class of semilinear parabolic equations with a gradient term. J. Nonlinear Sci. Appl. (2017); 10(4):1603--1612
Chicago/Turabian Style
Nie, Yuanyuan, Zhou, Mingjun, Zhou, Qian, Na, Yang. "Fujita type theorems for a class of semilinear parabolic equations with a gradient term." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1603--1612
Keywords
- Critical Fujita exponent
- gradient term.
MSC
References
-
[1]
J. Aguirre, M. Escobedo, On the blow-up of solutions of a convective reaction diffusion equation, Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), 433–460.
-
[2]
D. Andreucci, G. R. Cirmi, S. Leonardi, A. F. Tedeev, Large time behavior of solutions to the Neumann problem for a quasilinear second order degenerate parabolic equation in domains with noncompact boundary, J. Differential Equations, 174 (2001), 253–288.
-
[3]
K. Deng, H. A. Levine, The role of critical exponents in blow-up theorems: the sequel, J. Math. Anal. Appl., 243 (2000), 85–126.
-
[4]
M. Fira, B. Kawohl, Large time behavior of solutions to a quasilinear parabolic equation with a nonlinear boundary condition, Adv. Math. Sci. Appl., 11 (2001), 113–126.
-
[5]
A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1964)
-
[6]
H. Fujita, On the blowing up of solutions of the Cauchy problem for \(u_t=\Delta u+u^{1+\alpha}\) , J. Fac. Sci. Univ. Tokyo Sect. I, 13 (1966), 109–124.
-
[7]
H. A. Levine, The role of critical exponents in blowup theorems, SIAM Rev., 32 (1990), 262–288.
-
[8]
H. A. Levine, Q. S. Zhang, The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values, Proc. Roy. Soc. Edinburgh Sect. A, 130 (2000), 591–602.
-
[9]
P. Meier, On the critical exponent for reaction-diffusion equations, Arch. Rational Mech. Anal., 109 (1990), 63–71.
-
[10]
Y.-W. Qi, The critical exponents of parabolic equations and blow-up in /(R^n\), Proc. Roy. Soc. Edinburgh Sect. A, 128 (1998), 123–136.
-
[11]
Y.-W. Qi, M.-X. Wang, Critical exponents of quasilinear parabolic equations, J. Math. Anal. Appl., 267 (2002), 264–280.
-
[12]
Z.-J. Wang, J.-X. Yin, C.-P. Wang, Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition, Appl. Math. Lett., 20 (2007), 142–147.
-
[13]
C.-P. Wang, S.-N. Zheng, Critical Fujita exponents of degenerate and singular parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 136 (2006), 415–430.
-
[14]
C.-P. Wang, S.-N. Zheng, Fujita-type theorems for a class of nonlinear diffusion equations, Differential Integral Equations, 26 (2013), 555–570.
-
[15]
C.-P. Wang, S.-N. Zheng, Z.-J. Wang, Critical Fujita exponents for a class of quasilinear equations with homogeneous Neumann boundary data, Nonlinearity, 20 (2007), 1343–1359.
-
[16]
M. Winkler, A critical exponent in a degenerate parabolic equation, Math. Methods Appl. Sci., 25 (2002), 911–925.
-
[17]
Q. S. Zhang, A general blow-up result on nonlinear boundary-value problems on exterior domains, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 451–475.
-
[18]
S.-N. Zheng, X.-F. Song, Z.-X. Jiang, Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl., 298 (2004), 308–324.
-
[19]
S.-N. Zheng, C.-P. Wang, Large time behaviour of solutions to a class of quasilinear parabolic equations with convection terms, Nonlinearity, 21 (2008), 2179–2200.
-
[20]
Q. Zhou, Y.-Y. Nie, X.-Y. Han, Large time behavior of solutions to semilinear parabolic equations with gradient, J. Dyn. Control Syst., 22 (2016), 191–205.
