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arXiv · 1710.08959

Decay Estimates for Solutions of Porous Medium Equations with Advection

Nicolau Matiel Lunardi Diehl·Lucineia Fabris·Juliana Sartori Ziebell
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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\,|^α \, \nabla u \;\!), \quad \;\; x \in \mathbb{R}^{n}\!\:\!, \; t > 0, \end{equation} where $ α> 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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Nicolau Matiel Lunardi Diehl, Lucineia Fabris, Juliana Sartori Ziebell. 2019-03-13. Decay Estimates for Solutions of Porous Medium Equations with Advection. https://doi.org/10.1007/s10440-019-00246-4

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