Finite Time Blow-up for a Non-linear Parabolic Equation with a Gradient Term and Applications

1996 ◽  
Vol 19 (16) ◽  
pp. 1317-1333 ◽  
Author(s):  
Philippe Souplet
Keyword(s):  
Parabolic Equation ◽  
Finite Time ◽  
Blow Up ◽  
Linear Parabolic Equation ◽  
Gradient Term ◽  
Non Linear

scholarly journals Initiation of thermal explosion by intense light: criticality dependence on data and parameters

1987 ◽  
Vol 28 (3) ◽  
pp. 287-295 ◽  
Author(s):  
K. K. Tam
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Steady State Solution ◽  
Linear Ordinary Differential Equation ◽  
Critical Parameters ◽  
Linear Parabolic Equation ◽  
Thermal Ignition ◽  
Non Linear ◽  
Intense Light

AbstractA model for thermal ignition by intense light is studied. The governing non-linear parabolic equation is linearized in a two-step manner with the aid of a non-linear ordinary differential equation which captures the salient features of the non-linear parabolic equation. The critical parameters are computed from the steady-state solution of the ordinary differential equation, which can be obtained without actually solving the equation. Comparison with available data shows that the present method yields good results.

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