Accurate numerical resolution of transients in initial-boundary value problems for the heat equation

2003 ◽  
Vol 184 (2) ◽  
pp. 526-539 ◽  
Author(s):  
Natasha Flyer ◽  
Bengt Fornberg
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Numerical Resolution ◽  
Initial Boundary Value

scholarly journals The profile near quenching time for the solution of a singular semilinear heat equation

1997 ◽  
Vol 40 (3) ◽  
pp. 437-456 ◽  
Author(s):  
Jong-Shenq Guo ◽  
Bei Hu
Keyword(s):  
Heat Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Quenching Rate ◽  
Semilinear Heat Equation ◽  
Self Similar ◽  
Initial Boundary Value ◽  
Quenching Time

We study the profile near quenching time for the solutions of the first and second initial boundary value problems (IBVP) for a semilinear heat equation. Under certain conditions, one-point quenching occurs for both first and second IBVPs. Furthermore, we derive the asymptotic self-similar quenching rate for both problems.

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