scholarly journals Non-simultaneous blow-up for a semilinear parabolic system with localized reaction terms

2012 ◽  
pp. 319-337
Author(s):  
Atsuko Okada
Keyword(s):  
Parabolic System ◽  
Blow Up ◽  
Semilinear Parabolic System ◽  
Semilinear Parabolic ◽  
Localized Reaction

scholarly journals A Class of Nonlocal Coupled Semilinear Parabolic System with Nonlocal Boundaries

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hong Liu ◽  
Haihua Lu
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Parabolic System ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Dirichlet Boundary Conditions ◽  
Nonlocal Sources ◽  
Semilinear Parabolic System ◽  
Semilinear Parabolic ◽  
Existence Criteria

We investigate the positive solutions of the semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. The blow-up and global existence criteria are obtained.

scholarly journals A Note on Parabolic Liouville Theorems and Blow-Up Rates for a Higher-Order Semilinear Parabolic System

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Guocai Cai ◽  
Hongjing Pan ◽  
Ruixiang Xing
Keyword(s):  
Parabolic System ◽  
Blow Up ◽  
Parabolic Systems ◽  
Time Variable ◽  
Liouville Type ◽  
Liouville Theorems ◽  
Semilinear Parabolic System ◽  
Liouville Type Theorems ◽  
Systems Of Inequalities ◽  
Semilinear Parabolic

We improve some results of Pan and Xing (2008) and extend the exponent range in Liouville-type theorems for some parabolic systems of inequalities with the time variable onR. As an immediate application of the parabolic Liouville-type theorems, the range of the exponent in blow-up rates for the corresponding systems is also improved.

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