Cahn–Hilliard equations on random walk spaces

DOI10.1142/s0219530523500045arXiv2207.12682MaRDI QIDQ6166165

José M. Mazón Ruiz, Julián Toledo

Publication date: 2 August 2023

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.12682

zbMATH Keywords

phase transitionmonotone operatorweighted graphsrandom walkCahn-Hilliard equationsnonlocal operators

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Markov semigroups and applications to diffusion processes (47D07) Applications of operator theory to differential and integral equations (47N20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics (82C24) Random walks on graphs (05C81) Integro-partial differential equations (35R09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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• Continuum limit of total variation on point clouds
• Gradient flow structures for discrete porous medium equations
• Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
• Nonlocal problems with Neumann boundary conditions
• Local asymptotics for nonlocal convective Cahn-Hilliard equations with \(W^{1,1}\) kernel and singular potential
• Nonlocal discrete \(p\)-Laplacian driven image and manifold processing
• Ricci curvature of Markov chains on metric spaces
• Phase segregation dynamics in particle systems with long range interactions. I: Macroscopic limits
• On a nonlocal phase separation model
• Doubly nonlocal Cahn-Hilliard equations
• Optimal boundary control of a nonstandard Cahn-Hilliard system with dynamic boundary condition and double obstacle inclusions
• The Neumann boundary problem for a nonlocal Cahn-Hilliard equation
• The nonlocal Cahn-Hilliard equation with singular potential: well-posedness, regularity and strict separation property
• Three-dimensional multispecies nonlinear tumor growth. I: Model and numerical method
• Gradient flows in metric random walk spaces
• Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics
• Nonlocal-to-local convergence of Cahn-Hilliard equations: Neumann boundary conditions and viscosity terms
• Ollivier's Ricci curvature, local clustering and curvature-dimension inequalities on graphs
• The heat flow on metric random walk spaces
• The total variation flow in metric random walk spaces
• The Cahn-Hilliard equation and some of its variants
• Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplace operator
• Nonlinear semigroups in Hilbert space
• Nonlocal doubly nonlinear diffusion problems with nonlinear boundary conditions
• Cahn-Hilliard equations governed by weakly nonlocal conservation laws and weakly nonlocal particle interactions
• A Cahn–Hilliard–Darcy model for tumour growth with chemotaxis and active transport
• Consistency of Cheeger and Ratio Graph Cuts
• Inpainting of Binary Images Using the Cahn–Hilliard Equation
• Lectures on Optimal Transport
• On a nonlocal Cahn–Hilliard model permitting sharp interfaces
• Continuum Limits of Nonlocal $p$-Laplacian Variational Problems on Graphs
• The Cahn–Hilliard Equation: Recent Advances and Applications
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Generation of Semi-Groups of Nonlinear Transformations on General Banach Spaces
• Nonlinear Differential Equations of Monotone Types in Banach Spaces

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