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Tumor growth with nutrients: stability of the tumor patches
Inwon Kim, Jona Lelmi
In this paper, we study a tumor growth model with nutrients. The contact inhibition for the tumor cells, presented in the model, results in the evolution of a congested tumor patch…
Large data limit of the MBO scheme for data clustering: convergence of the dynamics
Tim Laux, Jona Lelmi
We prove that the dynamics of the MBO scheme for data clustering converge to a viscosity solution to mean curvature flow. The main ingredients are (i) a new abstract convergence re…
Large data limit of the MBO scheme for data clustering: -convergence of the thresholding energies
Tim Laux, Jona Lelmi
In this work we begin to rigorously analyze the MBO scheme for data clustering in the large data limit. Each iteration of the MBO scheme corresponds to one step of implicit gradien…
De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions
Tim Laux, Jona Lelmi
We provide a new convergence proof of the celebrated Merriman-Bence-Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general cl…