Anyin XIA
,
Mingshu FAN
,
Shan LI
. BLOW-UP AND LIFE SPAN ESTIMATES FOR A CLASS OF NONLINEAR DEGENERATE PARABOLIC SYSTEM WITH TIME-DEPENDENT COEFFICIENTS[J]. Acta mathematica scientia, Series B, 2017
, 37(4)
: 974
-984
.
DOI: 10.1016/S0252-9602(17)30052-8
[1] Deng W B. Global existence and finite time blow up for a degenerate reaction-diffusion system. Nonlinear Anal, 2005, 60:977-991
[2] Du L L, Mu C L, Fan M S. Global existence and non-existence for a quasilinear degenerate parabolic system with non-local source. Dyn Syst, 2005, 20:401-412
[3] Du L L. Blow-up for a degenerate reaction-diffusion system with nonlinear localized sources. J Math Anal Appl, 2006, 324:304-320
[4] Du L L. Blow-up for a degenerate reaction-diffusion system with nonlinear nonlocal sources. J Comput Appl Math, 2007, 202:237-247
[5] Du L L, Mu C L. Global existence and blow-up analysis to a degenerate reaction-diffusion system with nonlinear memory. Nonlinear Anal Real World Appl, 2008, 9:303-315
[6] Du L L, Xiang Zhaoyin. A further blow-up analysis for a localized porous medium equation. Appl Math Comput, 2006, 179:200-208
[7] Du L L, Yao Z A. Localization of blow-up points for a nonlinear nonlocal porous medium equation. Comm Pure Appl Anal, 2007, 6:183-190
[8] Du L L, Yao Z A. Note on non-simultaneous blow-up for a reaction-diffusion system. Appl Math Lett, 2008, 21:81-85
[9] Fan M S, Mu C L, Du L L. Uniform blow-up profiles for a nonlocal degenerate parabolic system. Appl Math Sci, 2007, 1:13-23
[10] Friedman A, Mcleod B. Blow-up of solutions of nonlinear degenerate parabolic equations. Arch Rational Mech Anal, 1986, 96(1):55-80
[11] Fujita H. On the blowing up of solutions of the Cauchy problem for ut=△u+u1+α. J Fac Sci Univ Tokyo Sect, 1966, 113:109-124
[12] Hernndez J, Mancebo F, Vega J. Positive solutions for singular nonlinear elliptic equation. Proc Roy Soc Edinburgh Sect, 2007, 137(1):41-62
[13] Hu Y, Wang L W, Chen X C. Lower bounds for blow-up time of porous medium equation with nonlinear flux on boundary. Int J Math Anal (Ruse), 2013, 7:2671-2676
[14] Li F C, Xie C H. Global existence and blow-up for a nonlinear porous medium equation. Appl Math Lett, 2003, 16:185-192
[15] Marras M, Vernier Piro S. Explicit estimates for blow-up solutions to parabolic systems with time dependent coefficients. Comtes Rendus de l'Academie Bulgare des Sciences, 2014, 67:459-466
[16] Mu C L, Hu X G, Li Y H, Cui Z J. Blow-up and global existence for a coupled system of degenerate parabolic equations in a bounded clomain. Acta Math Sci, 2007, 27B(1):92-106
[17] Payne L E, Schaefer P W. Lower bound for blow-up time in parabolic System under Dirichlet conditions. J Math Anal Appl, 2007, 328:1196-1205
[18] Payne L E, Philippin G A. Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Proc Amer Math Soc, 2013, 141(7):2309-2318
[19] Payne L E, Philippin G A. Blow-up phenamena for a class of Parabolic System with time dependent coefficients. Appl Math, 2012, 3:325-330
[20] Quittner P, Souplet P. Superlinear Parabolic Problems. Blow-up, Global Existence and Steady States. Basel:Birkhäuser, 2007
[21] Talenti G. Best constant in Sobolev inequality. Annali di Matematica Pura ed Applicata, 1976, 110:352-372
[22] Viglialoro G. Explicit blow-up time for complete porous medium problems. Proceeddings of the XXIV Congress on Equations and Applications, 2015, 7(8/12):821-826
[23] Weissler F B. Existence and nonexistence of global solutions for a heat equation. Israël J Math, 1981, 38(1/2):29-40
[24] Weigner M. A degenerate difussion equation with a nonlinear source term. Nonlinear Anal TMA, 1997, 28:1977-1995
[25] Xia A Y, Pu X X, Li S. Global existence and nonexistence for a class of parabolic systems with timedependent coefficients. Boundary Value Problems, 2016, 1:1-12