Abstract :
This work concerns a nonlinear diffusion]absorption equation with nonlinear
boundary flux. The main topic of interest is the problem of finite time extinction,
i.e., the solutions vanish after a finite time. The sufficient and necessary conditions
for occurrence of extinction are established. It is shown that extinction is caused by
either strong absorption in the interior of the domain or fast diffusion combined
with strong absorption through the boundary of the domain. Extinction results are
also obtained for the mixed boundary value problem. In contrast to the nonlinear
Neumann problem, the absorption on the boundary is no longer important, i.e., the
occurrence of extinction in this case is completely determined by the effects of
diffusion and interior absorption.
