Controllability for semilinear heat equation with globally Lipschitz nonlinearities and memory term

2021 ◽  
Vol 60 ◽  
pp. 103277
Author(s):  
I.P. de Jesus ◽  
A.M. Oliveira ◽  
M.R. Clark ◽  
P.P.A. Oliveira
Keyword(s):  
Heat Equation ◽  
Memory Term ◽  
Semilinear Heat Equation

scholarly journals Blow-up of solutions of a semilinear heat equation with a memory term

2005 ◽  
Vol 2005 (2) ◽  
pp. 87-94 ◽  
Author(s):  
Salim A. Messaoudi
Keyword(s):  
Boundary Value Problem ◽  
Heat Equation ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Energy ◽  
Memory Term ◽  
Semilinear Heat Equation ◽  
Positive Initial Energy ◽  
Initial Boundary Value

We consider an initial boundary value problem related to the equationut−Δu+∫0tg(t−s)Δu(x,s)ds=|u|p−2uand prove, under suitable conditions ongandp, a blow-up result for certain solutions with positive initial energy.

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