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Deadcore rates for the porous medium equation with a strong absorption
1.  Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260 
2.  Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137 
3.  Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556 
References:
[1] 
C. Bandle, T. Nanbu and I. Stakgold, Porous medium equation with absorption, SIAM J. Math. Anal., 29 (1998), 12681278. doi: 10.1137/S0036141096311423. 
[2] 
C. Bandle and I. Stakgold, The formation of the dead core in parabolic reactiondiffusion problems, Trans. Amer. Math. Soc., 286 (1984), 275293. doi: 10.1090/S00029947198407560401. 
[3] 
Q. Chen and L. Wang, On the dead core behavior for a semilinear heat equation, Math. Appl. (Wuhan), 10 (1997), 2225. 
[4] 
J.S. Guo and B. Hu, Quenching profile for a quasilinear parabolic equation, Quarterly Appl. Math., 58 (2000), 613626. 
[5] 
J.S. Guo, C.T. Ling and Ph. Souplet, Nonselfsimilar deadcore rate for the fast diffusion equation with strong absorption, Nonlinearity, 23 (2010), 657673. doi: 10.1088/09517715/23/3/013. 
[6] 
J.S. Guo, H. Matano and C.C. Wu, An application of braid group theory to the finite time deadcore rate, J. Evolution Equations, 10 (2010), 835855. doi: 10.1007/s0002801000720. 
[7] 
J.S. Guo and Ph. Souplet, Fast rate of formation of deadcore for the heat equation with strong absorption and applications to fast blowup, Math. Ann., 331 (2005), 651667. doi: 10.1007/s0020800406017. 
[8] 
J.S. Guo and C.C. Wu, Finite time deadcore rate for the heat equation with a strong absorption, Tohoku Math. J. (2), 60 (2008), 3770. doi: 10.2748/tmj/1206734406. 
[9] 
Y. Seki, On exact deadcore rates for a semilinear heat equation with strong absorption, Commun. Contemp. Math., 13 (2011), 152. 
[10] 
I. Stakgold, Reactiondiffusion problems in chemical engineering, in "Nonlinear Diffusion Problems" (Montecatini Terme, 1985), Lecture Notes in Math., 1224, Springer, Berlin, (1986), 119152. 
[11] 
T. I. Zelenjak, Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable, Differential Equations, 4 (1968), 1722. 
show all references
References:
[1] 
C. Bandle, T. Nanbu and I. Stakgold, Porous medium equation with absorption, SIAM J. Math. Anal., 29 (1998), 12681278. doi: 10.1137/S0036141096311423. 
[2] 
C. Bandle and I. Stakgold, The formation of the dead core in parabolic reactiondiffusion problems, Trans. Amer. Math. Soc., 286 (1984), 275293. doi: 10.1090/S00029947198407560401. 
[3] 
Q. Chen and L. Wang, On the dead core behavior for a semilinear heat equation, Math. Appl. (Wuhan), 10 (1997), 2225. 
[4] 
J.S. Guo and B. Hu, Quenching profile for a quasilinear parabolic equation, Quarterly Appl. Math., 58 (2000), 613626. 
[5] 
J.S. Guo, C.T. Ling and Ph. Souplet, Nonselfsimilar deadcore rate for the fast diffusion equation with strong absorption, Nonlinearity, 23 (2010), 657673. doi: 10.1088/09517715/23/3/013. 
[6] 
J.S. Guo, H. Matano and C.C. Wu, An application of braid group theory to the finite time deadcore rate, J. Evolution Equations, 10 (2010), 835855. doi: 10.1007/s0002801000720. 
[7] 
J.S. Guo and Ph. Souplet, Fast rate of formation of deadcore for the heat equation with strong absorption and applications to fast blowup, Math. Ann., 331 (2005), 651667. doi: 10.1007/s0020800406017. 
[8] 
J.S. Guo and C.C. Wu, Finite time deadcore rate for the heat equation with a strong absorption, Tohoku Math. J. (2), 60 (2008), 3770. doi: 10.2748/tmj/1206734406. 
[9] 
Y. Seki, On exact deadcore rates for a semilinear heat equation with strong absorption, Commun. Contemp. Math., 13 (2011), 152. 
[10] 
I. Stakgold, Reactiondiffusion problems in chemical engineering, in "Nonlinear Diffusion Problems" (Montecatini Terme, 1985), Lecture Notes in Math., 1224, Springer, Berlin, (1986), 119152. 
[11] 
T. I. Zelenjak, Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable, Differential Equations, 4 (1968), 1722. 
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