International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 427-434
doi:10.1155/S0161171296000610

Anisotropic nonlinear diffusion with absorption: Existence and extinction

Abstract

The authors prove that the nonlinear parabolic partial differential equation ∂u∂t=∑i,j=1n∂2∂xi∂xjφij(u)−f(u) 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.