BLOW-UP TIME OF SOLUTIONS FOR

SOME NONLINEAR PARABOLIC EQUATIONS

SOME NONLINEAR PARABOLIC EQUATIONS

Diabate Nabongo^{1}, N'Guessan Koffi^{2}, Toure Kidjegbo Augustin^{3}

^{1,2}Alassane Ouattara University of Bouake

UFR SED

Bouake, P.O.Box V18 Bouake, IVORY COST

^{3}National Polytechnic Institute Houphouet Boigny

Department of Mathematics

Yamoussoukro - P.O.Box 1093, IVORY COST

UFR SED

Bouake, P.O.Box V18 Bouake, IVORY COST

Department of Mathematics

Yamoussoukro - P.O.Box 1093, IVORY COST

where , , for , is a positive parameter, is a bounded domain in with smooth boundary , is positive, nondecreasing, convex function for positive values of and . We show that if is small enough, the solution of the above problem blows up in a finite time and its blow-up time tends to the one of the solution of the following differential equation

as goes to zero, where .

Finally, we give some numerical results to illustrate our analysis.

Download full article from here (pdf format).