Blow-up for Semidiscretization of Semilinear Parabolic Equation With Nonlinear Boundary Condition


  •  Ardjouma Ganon    
  •  Manin Mathurin Taha    
  •  Kidjégbo Augustin Touré    

Abstract

This paper deals with the study of the numerical approximation for the following semilinear equation with a nonlinear absorption term ut = uxx− λup, 0 < x < 1, t > 0, and a nonlinear flux boundary condition ux(0,t) = 0, ux(1,t) = uq(1,t), t > 0. We give conditions under which the positive semidiscrete solution blows up in a finite time. Convergence of the numerical blow-up time to the theoretical one when the mesh size goes to zero is established. Finally, we use an efficient algorithm to estimate the blow-up time.



This work is licensed under a Creative Commons Attribution 4.0 License.
  • ISSN(Print): 1916-9795
  • ISSN(Online): 1916-9809
  • Started: 2009
  • Frequency: bimonthly

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