Existence and Decay of Solutions of Some Nonlinear Degenerate Parabolic Equations

Abstract

We study the existence and the decay estimates of solutions of the initial-boundary value problem for some nonlinear degenerate parabolic equations

$${u_t} = \Delta \left( {{{\left| u \right|}^{m - 1}}u} \right) + b\cdot \nabla \left( {B\left( u \right)} \right) - q\left( t \right)A\left( u \right)$$

where u = u(x, t) is a scalar function of the spatial variable x ∈ Q and time t > 0,b ∈ R ^N(b ≠ O)and Ω is a regular unbounded domain in R ^N.