Large time behavior of solutions to Newtonian filtration equations with sources

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration with 0 < m < 1, p > 1, λ ≥ 0, k ∈ ℝ. An interesting phenomenon is that there exist two thresholds k∞ and k1 for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k ∈ (k∞, k1), otherwise, pc is infinite or does not exist.