scholarly journals CONTINUITY OF THE BLOW-UP TIME IN A NONLINEAR PARABOLIC EQUATION WITH NONLINEAR MEMORY

2021 ◽  
Vol 20 (1) ◽  
pp. 55-75
Author(s):  
N’gohisse Konan Firmin ◽  
Camara Zié ◽  
Yoro Gozo
Keyword(s):  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Blow Up ◽  
Nonlinear Memory ◽  
Nonlinear Parabolic

Convergence of blow-up solutions of nonlinear heat equations in the supercritical case

1999 ◽  
Vol 129 (6) ◽  
pp. 1197-1227 ◽  
Author(s):  
J. Matos
Keyword(s):  
Parabolic Equation ◽  
Heat Equation ◽  
Convergence Theorem ◽  
Nonlinear Parabolic Equation ◽  
Blow Up ◽  
Heat Equations ◽  
Semilinear Heat Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Heat Equations ◽  
Self Similar

In this paper, we study the blow-up behaviour of the radially symmetric non-negative solutions u of the semilinear heat equation with supercritical power nonlinearity up (that is, (N – 2)p> N + 2). We prove the existence of non-trivial self-similar blow-up patterns of u around the blow-up point x = 0. This result follows from a convergence theorem for a nonlinear parabolic equation associated to the initial one after rescaling by similarity variables.

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