Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: B. Yekre, Halima Nachid and Yoro Gozo
Pages: [1] - [37]
Received Date: January 26, 2019; Revised March 18, 2019
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122030
In this paper, we consider the following initial-boundary value
problem:
where 
is a positive, increasing, convex function for
nonnegative value of 
and 
is a positive diffusion parameter. We find some
conditions under which the solution of semidiscrete form of the above
problem blows up in a finite time and estimate its semidiscrete
blow-up time. We also prove the convergence of the semidiscrete form
blow-up time to the real one when the mesh size tends to zero.
Finally, we give some numerical results to illustrate our analysis.
diffusion parameter, reaction-diffusion equation, blow-up time, semidiscretization, convergence.
