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• W2037687788 abstract "We study weighted porous media equations on domains $Omegasubseteq{mathbb R}^N$, either with Dirichlet or with Neumann homogeneous boundary conditions when $Omeganot={mathbb R}^N$. Existence of weak solutions and uniqueness in a suitable class is studied in detail. Moreover, $L^{q_0}$-$L^varrho$ smoothing effects ($1leq q_0<varrho<infty$) are discussed for short time, in connection with the validity of a Poincar'e inequality in appropriate weighted Sobolev spaces, and the long-time asymptotic behaviour is also studied. Particular emphasis is given to the Neumann problem, which is much less studied in the literature, as well as to the case $Omega={mathbb R}^N$ when the corresponding weight makes its measure finite, so that solutions converge to their weighted average instead than to zero. Examples are given in terms of wide classes of weights." @default.
• W2037687788 created "2016-06-24" @default.
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• W2037687788 date "2012-04-27" @default.
• W2037687788 modified "2023-09-27" @default.
• W2037687788 title "Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincar'e inequalities" @default.
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