Blow-up in Quasilinear Heat Equations Described by Hamilton—Jacobi Equations

2004 ◽  
pp. 265-298
Author(s):  
Victor A. Galaktionov ◽  
Juan Luis Vázquez
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Jacobi Equations

scholarly journals Blow-Up for Quasilinear Heat Equations Described by Means of Nonlinear Hamilton–Jacobi Equations

1996 ◽  
Vol 127 (1) ◽  
pp. 1-40 ◽  
Author(s):  
Victor A. Galaktionov ◽  
Juan L. Vazquez
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Jacobi 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.

Sign in / Sign up

Export Citation Format

Share Document