This paper concerns the study of the extinction time of the solution of the following initial-boundary value problem
[left{%
begin{array}{ll}
hbox{ut=varepsilonLu(x,t)−f(u)quadmboxinquadOmegatimesmathbbR+,} \
hbox{u(x,t)=0quadmboxonquadpartialOmegatimesmathbbR+,} \
hbox{u(x,0)=u0(x)>0quadmboxinquadOmega,} \
end{array}%right. ]
where Omega is a bounded domain in mathbbRN with smooth boundary partialOmega, varepsilon is a positive parameter, f(s) is a positive, increasing, concave function for positive values of s, f(0)=0, int0fracdsf(s)<+infty, L is an elliptic operator. We show that the solution of the above problem extincts in a finite time and its extinction time goes to that of the solution alpha(t) of the following differential equation
[alpha^{\u27}(t)=-f(alpha(t)),quad t>0,quad alpha(0)=M,] as
varepsilon goes to zero, where M=supxinOmegau0(x).
We also extend the above result to other classes of nonlinear
parabolic equations. Finally, we give some numerical results to
illustrate our analysis