Contributions to Books:
A. Jüngel, I. Violet:
"Mixed entropy eatimates for the porous-medium equation with convection";
in: "ASC Report 33/2008",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
In this paper, we answer the question under which conditions the porousmedium
equation with convection and with periodic boundary conditions possesses gradient-
type Lyapunov functionals (first-order entropies). It is shown that the weighted
sum of first-order and zeroth-order entropies are Lyapunov functionals if the weight for
the zeroth-order entropy is sufficiently large, depending on the strength of the convection.
This provides new a priori estimates for the convective porous-medium equation. The
proof is based on an extension of the algorithmic entropy construction method which is
based on systematic integration by parts, formulated as a polynomial decision problem.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.