Displaying similar documents to “Weak and classical solutions of equations of motion for third grade fluids”

Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting

Xiaobing Feng, Andreas Prohl (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper studies the gradient flow of a regularized Mumford-Shah functional proposed by Ambrosio and Tortorelli (1990, 1992) for image segmentation, and adopted by Esedoglu and Shen (2002) for image inpainting. It is shown that the gradient flow with initial data possesses a global weak solution, and it has a unique global in time strong solution, which has at most finite number of point singularities in the space-time, when the initial data are in . A family of fully discrete...

Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces

Stefano Lisini (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We study existence and approximation of non-negative solutions of partial differential equations of the type 
 t u - div ( A ( ( f ( u ) ) + u V ) ) = 0 in ( 0 , + ) × n , ( 0 . 1 ) where is a symmetric matrix-valued function of the spatial variable satisfying a uniform ellipticity condition, f : [ 0 , + ) [ 0 , + ) is a suitable non decreasing function, V : n is a convex function. Introducing the energy functional φ ( u ) = n F ( u ( x ) ) d x + n V ( x ) u ( x ) d x , where is a convex function linked to by f ( u ) = u F ' ( u ) - F ( u ) , we show that is the “gradient flow” of with respect to the 2-Wasserstein distance between probability measures on the...