BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

doi:10.1016/S0252-9602(13)60060-0

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35K55

WU Xiu-Lan, GAO Wen-Jie. BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY[J].Acta mathematica scientia,Series B, 2013, 33(4): 1024-1030.

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[1] Wu Z Q, Zhao J N, Yin J X, Li H L. Nonlinear Diffusion Equations. Singapore: World Scientific, 2001

[2] Galaktionov V A, Vazquez J L. The problem of blow-up in nonlinear parabolic equations. Discrete Contin Dynam System, 2002, 8(2): 399–433

[3] Ferreira R, Vazquez J L. Extinction behavior for fast diffusion equations with absorption. Nonlinear Anal, 2001, 43: 943–985

[4] Li Y X, Wu J C. Extinction for fast diffusion equations with nonlinear sources. Electron J Differ Equ, 2005, 23: 1–7

[5] Han Y Z, Gao W J. Extinction for a fast diffusion equation with a nonlinear nonlocal source. Arch Math, 2011, 97: 353–363

[6] Peietier L A, Junning Z. Source-type solutions of porous media equation with absorption: The fast diffusion case. Nonlinear Anal, 1991, 17: 991–1009

[7] Leoni G. A very singular solution for the porous media equation u_t= Δu^m− up when 0 < m < 1. J Diff Equ, 1996, 132: 353–376

[8] Mochizuki K, Suzuki R. Critical exponent and critical blow up for quasi-linear parabolic equations. Israel J Math, 1997, 98: 141–156

[9] Mu C L, Zeng R, Chen B T. Blow-up phenomena for a doubly degenerate equation with positive initial energy. Nonlinear Anal, 2010, 72: 782–793

[10] Liu W J, Wang M X. Blow-up of the solution for a p-Laplaican equation with positive initial energy. Acta Appl Math, 2008, 103: 141–146

[11] Gao W J, Han Y Z. Blow-up of a nonlocal semilinear parabolic equation with positive initial energy. Appl Math Lett, 2011, 24: 784–788

[12] Wang J, Gao W J. Existence of solutions to a class of doubly degenerate equations and blow up with vanishing intial energy. J Math Res Exposition, 2007, 27: 161–168 (in Chinese)

[13] Ladyzenskaja O, Solonnikov V, Uraltseva N. Linear and Quasilinear Equations of Parabolic Type. Transl Math Monogr. Providence, RI: American Mathematical Society, 1968

[14] Zhong C K, Fan X L, Chen W Y. Nonlinear Functinal Analysis. Lanzhou: Lanzhou University Press, 2004 (in Chinese)

[15] Vitillaro E. Global nonexistence theorems for a class of evolution equations with dissipation. Arch Ration Mech Anal, 1999, 149: 155–182

[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 domain. Acta Math Sci, 2007, 27B(1): 92–106

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

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