Eventual B-convexity: a Criterion of Complete Blow-up and Extinc- tion for Quasilinear Heat Equations

2004 ◽  
pp. 127-146
Keyword(s):  
Blow Up ◽  
Heat Equations

scholarly journals Blow-up of solutions of nonlinear heat equations

1988 ◽  
Vol 129 (2) ◽  
pp. 409-419 ◽  
Author(s):  
Luis A. Caffarrelli ◽  
Avner Friedman
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Nonlinear Heat Equations

scholarly journals A blow-up dichotomy for semilinear fractional heat equations

2020 ◽  
Author(s):  
Robert Laister ◽  
Mikołaj Sierżęga
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Positive Solutions ◽  
Finite Time ◽  
Blow Up ◽  
Heat Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Whole Space ◽  
Necessary And Sufficient

Abstract We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive solutions to become unbounded in finite time. Moreover, we show that this condition is equivalent to blow-up of all positive solutions of a closely-related scalar ordinary differential equation.

Non-simultaneous blow-up in coupled heat equations with multi-nonlinearities

2009 ◽  
Vol 70 (12) ◽  
pp. 4165-4177
Author(s):  
Sining Zheng ◽  
Jing Ma
Keyword(s):  
Blow Up ◽  
Heat Equations
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