Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure
Copyright policy )Modified Wasserstein gradient flow formulation of time-fractional porous medium equations with nonlocal pressure
We consider a class of time-fractional porous medium equations with nonlocal pressure. We show the existence of their weak solutions by proposing a JKO scheme for modified Wasserstein distance and a square fractional Sobolev norm. Moreover, the regularization effect and the Lp norm estimate are established in this paper.
modified Wasserstein distance, gradient flow, Quasilinear parabolic equations, Mathematics - Analysis of PDEs, Smoothness and regularity of solutions to PDEs, FOS: Mathematics, JKO scheme, time-fractional porous medium equation, fractional Laplacian, Degenerate parabolic equations, Fractional partial differential equations, Analysis of PDEs (math.AP)
modified Wasserstein distance, gradient flow, Quasilinear parabolic equations, Mathematics - Analysis of PDEs, Smoothness and regularity of solutions to PDEs, FOS: Mathematics, JKO scheme, time-fractional porous medium equation, fractional Laplacian, Degenerate parabolic equations, Fractional partial differential equations, Analysis of PDEs (math.AP)
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