scholarly journals Blow-up rate of solutions of parabolic poblems with nonlinear boundary conditions

2012 ◽  
Vol 5 (3) ◽  
pp. 671-681 ◽  
Author(s):  
Pavol Quittner ◽  
◽  
Philippe Souplet ◽  
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Blow Up Rate

scholarly journals Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions

2008 ◽  
Vol 2008 ◽  
pp. 1-29 ◽  
Author(s):  
Louis A. Assalé ◽  
Théodore K. Boni ◽  
Diabate Nabongo
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Analogous Result ◽  
Nonlinear Boundary Conditions ◽  
Semilinear Parabolic Equation ◽  
Discrete Form ◽  
Semilinear Equation ◽  
Blow Up Rate ◽  
Semilinear Parabolic

We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equationut=uxx−a(x,t)f(u),  0<x<1,  t∈(0,T), with boundary conditionsux(0,t)=0,ux(1,t)=b(t)g(u(1,t)), blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-up rate and set. Finally, we get an analogous result taking a discrete form of the above problem and give some computational results to illustrate some points of our analysis.

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