Extinction in finite time of solutions to nonlinear absorption-diffusion equations (Q1323924)

The authors obtain necessary and sufficient conditions for the extinction in a finite time of solutions to nonlinear absorption-diffusion equations of the type \[ u_ t= \Delta\varphi (u)- f(u) \qquad \text{in } \Omega\times (0,\infty), \] where \(\Omega\) is a domain (bounded or unbounded) in \(\mathbb{R}^ N\). They improve several previous results in the literature.