Abstract
In this paper, we study the initial boundary value problem of Newtonian filtration equation in a cone-like do main
, where
,
, with
. Let
denote the smallest Dirichlet eigenvalue for the Laplace–Beltrami operator on
and let l denote the positive root of
. We prove that if
, then the problem has no global nonnegative solutions for any nonnegative
unless
; if
, then the problem has global solutions for some
.
Acknowledgements
The authors would like to express their deep thanks to the referee’s valuable suggestions for the revision and improvement of the manuscript.
Notes
No potential conflict of interest was reported by the authors.