Finite time blow-up for a nonlocal in time nonlinear heat equation in an exterior domain

2020 ◽  
Vol 99 ◽  
pp. 105985 ◽  
Author(s):  
Mohamed Jleli ◽  
Besssem Samet
Keyword(s):  
Heat Equation ◽  
Finite Time ◽  
Exterior Domain ◽  
Blow Up ◽  
Nonlinear Heat 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.

NUMERICAL BLOW-UP FOR A NONLINEAR PROBLEM WITH A NONLINEAR BOUNDARY CONDITION

2002 ◽  
Vol 12 (04) ◽  
pp. 461-483 ◽  
Author(s):  
RAÚL FERREIRA ◽  
PABLO GROISMAN ◽  
JULIO D. ROSSI
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Nonlinear Problem ◽  
Finite Time ◽  
Numerical Scheme ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Nonlinear Heat Equation ◽  
Mesh Parameter

In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also find the blow-up rates and the blow-up sets. In particular we prove that regional blow-up is not reproduced by the numerical scheme. However, in the appropriate variables we can reproduce the correct blow-up set when the mesh parameter goes to zero.

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

Global Well-Posedness and Finite-Time Blow-Up of Some Heat-Type Equations

2016 ◽  
Vol 60 (2) ◽  
pp. 481-497 ◽  
Author(s):  
Tarek Saanouni
Keyword(s):  
Heat Equation ◽  
Finite Time ◽  
Blow Up ◽  
Type Equation ◽  
High Order ◽  
Energy Space ◽  
Well Posedness ◽  
Exponential Nonlinearity

AbstractWe study two different heat-type equations. First, global well-posedness in the energy space of some high-order semilinear heat-type equation with exponential nonlinearity is obtained for even space dimensions. Second, a finite-time blow-up result for the critical monomial focusing heat equation with the p-Laplacian is proved.

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