A Simplified Approach to the Refined Blowup Behavior for the Nonlinear Heat Equation

We consider radial decreasing solutions of the semilinear heat equation for subcritical, critical, and supercritical powers. We provide a much simpler and more pedagogical proof of the classical re...

[1]  Miguel A. Herrero,et al.  Blow-up behaviour of one-dimensional semilinear parabolic equations , 1993 .

[2]  N. Mizoguchi Nonexistence of backward self-similar blowup solutions to a supercritical semilinear heat equation , 2009 .

[3]  H. Zaag Determination of the curvature of the blow-up set and refined singular behavior for a semilinear heat equation , 2006 .

[4]  F. Merle,et al.  Refined Uniform Estimates at Blow-Up and Applications for Nonlinear Heat Equations , 1998 .

[5]  Hatem Zaag,et al.  Optimal estimates for blowup rate and behavior for nonlinear heat equations , 1998 .

[6]  P. Polácik,et al.  Singularity and decay estimates in superlinear problems via liouville-type theorems. Part II: Parabolic equations , 2007 .

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

[8]  J. J. L. Velázquez,et al.  Classification of singularities for blowing up solutions in higher dimensions , 1993 .

[9]  N. Mizoguchi Type-II blowup for a semilinear heat equation , 2004, Advances in Differential Equations.

[10]  On backward self-similar blow-up solutions to a supercritical semilinear heat equation , 2010, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[11]  N. Mizoguchi Nonexistence of type II blowup solution for a semilinear heat equation , 2011 .

[12]  Robert V. Kohn,et al.  Refined asymptotics for the blowup of ut –Δu = up , 1992 .

[13]  J. Velázquez Higher dimensional blow up for semilinear parabolic equations , 1992 .

[14]  Fred B. Weissler,et al.  Single point blow-up for a semilinear initial value problem , 1984 .

[15]  F. Merle,et al.  Threshold and generic type I behaviors for a supercritical nonlinear heat equation , 2011 .

[16]  J. Velázquez,et al.  Estimates on the (n−1)-dimensional Hausdorff measure of the blow-up set for a semilinear heat equation , 1992 .

[17]  Fred B. Weissler,et al.  An L∞ blow‐up estimate for a nonlinear heat equation , 1985 .

[18]  F. Merle,et al.  Classification of type I and type II behaviors for a supercritical nonlinear heat equation , 2009 .