Abstract
In this paper, we show that bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form \begin{equation} \notag u_t \,+\; \mbox{div}\,f(x,t,u) \;=\; \mbox{div}\,(\;\!|\,u\,|^{\alpha} \, \nabla u \;\!), \quad \;\; x \in \mathbb{R}^{n}\!\:\!, \; t > 0, \end{equation} where $ \alpha > 0 \, $ is constant, decrease to zero, under fairly broad conditions on the advection flux $f$. Besides that, we derive a time decay rate for these solutions.
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