The absence of global weak solutions for a quasilinear parabolic differential inequality in exterior domain

This paper is concerned with the absence of nontrivial nonnegative global weak solutions for a quasilinear parabolic differential inequality in the higher dimensional space ($N\geq2$). Assuming that the non-homogeneous Dirichlet boundary condition relies on both time and space, we derive a criterion of the absence which depends on the effects of quasilinear diffusion and the behavior of time-varying coefficient precisely.