Curves of steepest descent are entropy solutions for a class of degenerate convection–diffusion equations
Curves of steepest descent are entropy solutions for a class of degenerate convection–diffusion equations
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最速下降曲线是一类简并对流扩散方程的熵解
DOI：
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发表时间：
2012
影响因子：
2.1
通讯作者：
D. Matthes
中科院分区：
文献类型：
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作者：
M. Di Francesco;D. Matthes
We consider a nonlinear degenerate convection–diffusion equation with inhomogeneous convection and prove that its entropy solutions in the sense of Kružkov are obtained as the-a posteriori unique-limit points of the JKO variational approximation scheme for an associated gradient flow in the L2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2$$end{document}-Wasserstein space. The equation lacks the necessary convexity properties which would allow to deduce well-posedness of the initial value problem by the abstract theory of metric gradient flows. Instead, we prove the entropy inequality directly by variational methods and conclude uniqueness by doubling of the variables.
We consider a nonlinear degenerate convection–diffusion equation with inhomogeneous convection and prove that its entropy solutions in the sense of Kružkov are obtained as the—a posteriori unique—limit points of the JKO variational approximation scheme for an associated gradient flow in the L2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$L^2$$end{document}-Wasserstein space. The equation lacks the necessary convexity properties which would allow to deduce well-posedness of the initial value problem by the abstract theory of metric gradient flows. Instead, we prove the entropy inequality directly by variational methods and conclude uniqueness by doubling of the variables.