scholarly journals Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity

2020 ◽  
Vol 19 (2) ◽  
pp. 923-939
Author(s):  
Xiumei Deng ◽  
◽  
Jun Zhou
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Singular Potential ◽  
Blow Up ◽  
Semilinear Heat Equation

scholarly journals Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

2019 ◽  
Vol 53 (1) ◽  
pp. 57-72
Author(s):  
Marcos Josías Ceballos-Lira ◽  
Aroldo Pérez
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Mild Solution ◽  
Blow Up ◽  
Local Existence ◽  
Dirichlet Condition ◽  
Infinite Time ◽  
Diffusion Operator ◽  
Intrinsic Ultracontractivity ◽  
Semilinear Heat Equation

In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.

scholarly journals On global existence and bounds for the blow-up time in a semilinear heat equation involving parametric variable sources

2021 ◽  
Vol 349 (3) ◽  
pp. 519-527
Author(s):  
Rabil Ayazoglu (Mashiyev) ◽  
Ebubekir Akkoyunlu ◽  
Tuba Agirman Aydin
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Blow Up ◽  
Semilinear Heat Equation

scholarly journals Stability of ODE blow-up for the energy critical semilinear heat equation

2017 ◽  
Vol 355 (1) ◽  
pp. 65-79 ◽  
Author(s):  
Charles Collot ◽  
Frank Merle ◽  
Pierre Raphaël
Keyword(s):  
Heat Equation ◽  
Blow Up ◽  
Semilinear Heat Equation
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