Anisotropic nonlinear diffusion with absorption: existence and extinction

The authors prove that the nonlinear parabolic partial differential equation urn:x-wiley:01611712:media:ijmm347450:ijmm347450-math-0001 with homogeneous Dirichlet boundary conditions and a nonnegative initial condition has a nonnegative generalized solution u. They also give necessary and sufficient conditions on the constitutive functions φij and f which ensure the existence of a time t0 > 0 for which u vanishes for all t ≥ t0.