Dead-core rates for the fast diffusion equation with a spatially dependent strong absorption

AbstractThis paper deals with the dead-core rates problem for the fast diffusion equation with a spatially dependent strong absorption $$u_t=(u^{m})_{xx}-x^{q}u^p, \quad(x,t)\in(0,1)\times(0,\infty),$$ut=(um)xx-xqup,(x,t)∈(0,1)×(0,∞),where 0 < p < m < 1 and −1 < q < 0. By using the self-similar transformation technique and the Zelenyak method, we proved that the temporal dead-core rate is non-self-similar.

[1]  Victor A. Galaktionov,et al.  Extinction for a quasilinear heat equation with absorption I. Technique of intersection comparison , 1994 .

[2]  Biao Wang,et al.  Spatial Profile of the Dead Core for the Fast Diffusion Equation with Dependent Coefficient , 2011 .

[3]  Victor A. Galaktionov,et al.  Extinction for a quasilinear heat equation with absorption ii. a dynamical systems approach , 1994 .

[4]  Jong-Shenq Guo,et al.  Quenching profile for a quasilinear parabolic equation , 2000 .

[5]  Catherina Bandle,et al.  Estimates for solutions of quasilinear problems with dead cores , 2003 .

[6]  Miguel A. Herrero,et al.  Approaching an extinction point in one-dimensional semilinear heat equations with strong absorption , 1992 .

[7]  Hiroshi Matano,et al.  An application of braid group theory to the finite time dead-core rate , 2010 .

[8]  Jong-Shenq Guo,et al.  Fast rate of formation of dead-core for the heat equation with strong absorption and applications to fast blow-up , 2005 .

[9]  Catherine Bandle,et al.  The formation of the dead core in parabolic reaction-diffusion problems , 1984 .

[10]  Jong-Shenq Guo,et al.  DEAD-CORE AT TIME INFINITY FOR A HEAT EQUATION WITH STRONG ABSORPTION , 2009 .

[11]  Y. Qi.  The critical exponents of parabolic equations and blow-up in Rn , 1998, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[12]  Yukihiro Seki,et al.  On exact dead-core rates for a semilinear heat equation with strong absorption , 2011 .

[13]  Jong-Shenq Guo,et al.  Finite time dead-core rate for the heat equation with a strong absorption , 2008 .

[14]  Daniele Andreucci,et al.  Universal bounds at the blow-up time for nonlinear parabolic equations , 2005, Advances in Differential Equations.

[15]  Jong-Shenq Guo,et al.  Non-self-similar dead-core rate for the fast diffusion equation with strong absorption , 2010 .

[16]  Chin-Chin Wu,et al.  Dead-core rates for the heat equation with a spatially dependent strong absorption , 2013 .

[17]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[18]  A. Friedman,et al.  Blow-up of positive solutions of semilinear heat equations , 1985 .