scholarly journals Nonexistence of Positive Solutions to a Quasi-Linear Elliptic Equation and Blow-Up Estimates for a Nonlinear Heat Equation

2006 ◽  
Vol 36 (4) ◽  
pp. 1399-1414 ◽  
Author(s):  
Yang Zuodong
Keyword(s):  
Elliptic Equation ◽  
Heat Equation ◽  
Positive Solutions ◽  
Blow Up ◽  
Nonlinear Heat Equation ◽  
Linear Elliptic Equation

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.

Local well‐posedness and blow‐up for an inhomogeneous nonlinear heat equation

2020 ◽  
Vol 43 (8) ◽  
pp. 5264-5272
Author(s):  
Rasha Alessa ◽  
Aisha Alshehri ◽  
Haya Altamimi ◽  
Mohamed Majdoub
Keyword(s):  
Heat Equation ◽  
Blow Up ◽  
Nonlinear Heat Equation ◽  
Well Posedness
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