scholarly journals Improved conditions for single-point blow-up in reaction–diffusion systems

2015 ◽  
Vol 259 (5) ◽  
pp. 1898-1932 ◽  
Author(s):  
Nejib Mahmoudi ◽  
Philippe Souplet ◽  
Slim Tayachi
Keyword(s):  
Blow Up ◽  
Single Point ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

scholarly journals Blow-up phenomena in reaction-diffusion systems

2012 ◽  
Vol 32 (11) ◽  
pp. 4001-4014 ◽  
Author(s):  
Monica Marras ◽  
Stella Vernier Piro
Keyword(s):  
Blow Up ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

ON A NONLOCAL EIGENVALUE PROBLEM AND ITS APPLICATIONS TO POINT-CONDENSATIONS IN REACTION–DIFFUSION SYSTEMS

2000 ◽  
Vol 10 (06) ◽  
pp. 1485-1496 ◽  
Author(s):  
JUNCHENG WEI
Keyword(s):  
Eigenvalue Problem ◽  
Single Point ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Stability And Instability ◽  
Nonlocal Eigenvalue Problem

We consider a nonlocal eigenvalue problem which arises in the study of stability of point-condensation solutions in the Gierer–Meinhardt system and generalized Gray–Scott system. We give some sufficient conditions for stability and instability. The conditions are new and can be applied to the study of stability of single point-condensation solutions.

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