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DRIFT-DIFFUSION EQUATIONS WITH SATURATION
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DOI：10.1137/24M1706694.png)
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Abstract
En 中文
We focus on a family of nonlinear continuity equations for the evolution of a nonnegative density \rho with a continuous and compactly supported nonlinear mobility m(\rho) not necessarily concave. The velocity field is the negative gradient of the variation of a free energy including internal and confinement energy terms. Problems with compactly supported mobility are often called saturation problems since the values of the density are constrained below a maximal value. Taking advantage of a family of approximating problems, we show the existence of C0-semigroups of L1 contractions. We study the \omega-limit of the problem, its most relevant properties, and the appearance of free boundaries in the long-time behavior. This problem has a formal gradient-flow structure, and we discuss the local/global minimizers of the corresponding free energy in the natural topology related to the set of initial data for the Lo degrees-constrained gradient flow of probability densities. Furthermore, we analyze a structure preserving implicit finite-volume scheme and discuss its convergence and long-time behavior.
Keywords:
saturation
nonlinear parabolic equations
long-time behavior
C0-semigroup
free boundary
Euler--Lagrange condition
implicit finite-volume scheme
Journal
S
IF:
1.9
Papers:
96
Citations:
0