Two-sided estimates of a solution of the Neumann problem as $t \rightarrow \infty$ for a second-order Quasilinear Parabolic Equation

Abstract

We establish exact upper and lower bounds as $t \rightarrow \infty$ for the norm ‖u(·, t)‖ _{L ∞(Ω)} of a solution of the Neumann problem for a second-order quasilinear parabolic equation in the region D=Ω×{>0}, where Ω is a region with noncompact boundary.