Finite speed of propagation for the porous media equation with lower order terms

S. Bonafede; G. R. Cirmi; A.F. Tedeev

doi:10.3934/dcds.2000.6.305

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2000, Volume 6, Issue 2: 305-314. Doi: 10.3934/dcds.2000.6.305

This issue Previous Article Symbol sequences and entropy for piecewise monotone transformations with discontinuities Next Article Discontinuous elliptic problems in $R^N$: Lower and upper solutions and variational principles

Finite speed of propagation for the porous media equation with lower order terms

1.
Department E.S.A.F., University of Palermo, Viale delle Scienze, 90128 Palermo
2.
Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania
3.
Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Roza Luxemburg st.74, 340114 Donetsk

Received: July 31, 1997

Revised: April 30, 1999

Published: March 2000

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Abstract

We study the finite speed of propagation of the Cauchy-Dirichlet problem for the porous media equation with absorption or convection terms in the strip $\mathfrak R_k^N\times (0,T)$, where $\mathfrak R_k^N=\mathfrak R^N\cap\{x_1, ..., x_k>0\}$, $1\leq k\leq N $ and we find new upper bounds of the free boundary.
Finally, we consider the case of higher order parabolic equations.

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Mathematics Subject Classification: 34G10, 47D06, 58F11, 92D25.

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