A tumor growth model of Hele-Shaw type as a gradient flow
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Publication:5854396
DOI10.1051/cocv/2020019zbMath1460.92050arXiv1712.06124OpenAlexW3015436584MaRDI QIDQ5854396
Lénaïc Chizat, Simone Di Marino
Publication date: 17 March 2021
Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.06124
PDEs in connection with biology, chemistry and other natural sciences (35Q92) Other free boundary flows; Hele-Shaw flows (76D27) Pathology, pathophysiology (92C32)
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Cites Work
- Unnamed Item
- A fitness-driven cross-diffusion system from population dynamics as a gradient flow
- \{Euclidean, metric, and Wasserstein\} gradient flows: an overview
- From the Schrödinger problem to the Monge-Kantorovich problem
- Measure density and extendability of Sobolev functions
- A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions
- Quasiconformal mappings and extendability of functions in Sobolev spaces
- The geometry of optimal transportation
- Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
- A new optimal transport distance on the space of finite Radon measures
- Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures
- An interpolating distance between optimal transport and Fisher-Rao metrics
- Unbalanced optimal transport: dynamic and Kantorovich formulations
- Handling congestion in crowd motion modeling
- A Hele-Shaw problem for tumor growth
- Singular limit of the porous medium equation with a drift
- The Hele-Shaw asymptotics for mechanical models of tumor growth
- Sobolev embeddings, extensions and measure density condition
- A blob method for the aggregation equation
- Uniqueness issues for evolution equations with density constraints
- Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves
- Nonlinear Perron–Frobenius Theory
- A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE
- Scaling algorithms for unbalanced optimal transport problems
- An augmented Lagrangian approach to Wasserstein gradient flows and applications
- Strong convergence results related to strict convexity
- Entropic Approximation of Wasserstein Gradient Flows
- Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
- The Variational Formulation of the Fokker--Planck Equation
- Porous medium equation to Hele-Shaw flow with general initial density
- 13. Pressureless Euler equations with maximal density constraint: a time-splitting scheme
- An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems
- Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems
- Iterative Bregman Projections for Regularized Transportation Problems
- Gradient structures and geodesic convexity for reaction–diffusion systems
- A JKO Splitting Scheme for Kantorovich--Fisher--Rao Gradient Flows
- Convergence of Entropic Schemes for Optimal Transport and Gradient Flows
- Variational formulation for the lubrication approximation of the Hele-Shaw flow
- \(BV\) estimates in optimal transportation and applications
