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April  2000, 6(2): 305-314. doi: 10.3934/dcds.2000.6.305

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

S. Bonafede 1, , G. R. Cirmi 2, and  A.F. Tedeev 3,

1. 

Department E.S.A.F., University of Palermo, Viale delle Scienze, 90128 Palermo, Italy
2. 

Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy
3. 

Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Roza Luxemburg st.74, 340114 Donetsk, Ukraine

Received  August 1997 Revised  May 1999 Published  January 2000

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.
Keywords: age-structured population dynamics with another population structure., spectral bound, resolvent outputs, integrated semigroups, resolvent positive operator, growth bounds, cumulative outputs, Semigroups, eventual and essential compactness, Stieltjes integral equations, asynchronous exponential growth, positive perturbation.
Mathematics Subject Classification: 34G10, 47D06, 58F11, 92D2.
Citation: S. Bonafede, G. R. Cirmi, A.F. Tedeev. Finite speed of propagation for the porous media equation with lower order terms. Discrete & Continuous Dynamical Systems, 2000, 6 (2) : 305-314. doi: 10.3934/dcds.2000.6.305
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