Two theorems on blow-up solutions for semilinear parabolic equations of second order

1998 ◽  
Vol 327 (1) ◽  
pp. 47-52 ◽  
Author(s):  
Yuri V. Egorov ◽  
Vladimir A. Kondratiev
Keyword(s):  
Parabolic Equations ◽  
Blow Up ◽  
Second Order ◽  
Semilinear Parabolic Equations ◽  
Semilinear Parabolic

Global blow-up of a nonlinear heat equation

1986 ◽  
Vol 104 (1-2) ◽  
pp. 161-167 ◽  
Author(s):  
A. A. Lacey
Keyword(s):  
Heat Equation ◽  
Parabolic Equations ◽  
Finite Time ◽  
Positive Measure ◽  
Blow Up ◽  
Nonlinear Heat Equation ◽  
Semilinear Parabolic Equations ◽  
Semilinear Parabolic

SynopsisSolutions to semilinear parabolic equations of the form ut = Δu + f(u), x in Ω, which blow up at some finite time t* are investigated for “slowly growing” functions f. For nonlinearities such as f(s) = (2 +s)(ln(2 +s))1+b with 0 < b < l,u becomes infinite throughout Ω as t→t* −. It is alsofound that for marginally more quickly growing functions, e.g. f(s) = (2 + s)(ln(2 +s))2, u is unbounded on some subset of Ω which has positive measure, and is unbounded throughout Ω if Ω is a small enough region.

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