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Main Authors:	Riethmüller, Cedric, Storvik, Erlend, Both, Jakub Wiktor, Radu, Florin Adrian
Format:	Preprint
Published:	2023
Subjects:	Analysis of PDEs
Online Access:	https://arxiv.org/abs/2310.18231
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On the convergence and efficiency of splitting schemes for the Cahn-Hilliard-Biot model
by: Riethmüller, Cedric, et al.
Published: (2026)

Sharp-Interface Limit of the Cahn-Hilliard-Biot Equations
by: Storvik, Erlend, et al.
Published: (2024)

The Biot-Allard poro-elasticity system: equivalent forms and well-posedness
by: Stokke, Jakob S., et al.
Published: (2024)

Structure-preserving approximation of the Cahn-Hilliard-Biot system
by: Brunk, Aaron, et al.
Published: (2024)

Local Well-Posedness of the Cahn-Hilliard-Biot System
by: Abels, Helmut, et al.
Published: (2025)

On the well-posedness of the Cahn-Hilliard-Biot model and its applications to tumor growth
by: Fritz, Marvin
Published: (2023)

Well-posedness of Navier-Stokes/Cahn-Hilliard equations modeling the dynamics of contact line in a channel
by: Ding, Shijin, et al.
Published: (2023)

On the rate of convergence of Yosida approximation for the nonlocal Cahn-Hilliard equation
by: Gwiazda, Piotr, et al.
Published: (2023)

Comparison of Coarsening Dynamics for the Cahn--Hilliard and Burgers--Cahn--Hilliard Equations
by: Howard, Peter, et al.
Published: (2024)

Existence of Weak Solutions to a Cahn-Hilliard-Biot System
by: Abels, Helmut, et al.
Published: (2024)

Nonlocal-to-local convergence of the Cahn-Hilliard equation with degenerate mobility and the Flory-Huggins potential
by: Elbar, Charles, et al.
Published: (2024)

Partial Differential Equations in the Age of Machine Learning: A Critical Synthesis of Classical, Machine Learning, and Hybrid Methods
by: Nooraiepour, Mohammad, et al.
Published: (2026)

New results for the Cahn-Hilliard equation with non-degenerate mobility: well-posedness and longtime behavior
by: Conti, Monica, et al.
Published: (2024)

Global well-posedness of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with Landau Potential
by: Rui, Nie, et al.
Published: (2024)

On a stochastic Cahn-Hilliard-Brinkman model
by: Brzeźniak, Z., et al.
Published: (2026)

On a generalized Cahn-Hilliard model with p-Laplacian
by: Folino, Raffaele, et al.
Published: (2022)

Well-posedness of the nonhomogeneous incompressible Navier-Stokes/Allen-Cahn system
by: Li, Yinghua, et al.
Published: (2025)

Splitting-strategies for arbitrary-order fully mixed finite element discretizations of the Biot equations
by: Bertrand, Fleurianne, et al.
Published: (2026)

Well-posedness of three-dimensional Damped Cahn-Hilliard-Navier-Stokes Equations
by: Bag, Manika, et al.
Published: (2024)

Numerics and analysis of Cahn--Hilliard critical points
by: Grafke, Tobias, et al.
Published: (2021)

Low regularity potentials in heterogeneous Cahn--Hilliard functionals
by: Cristoferi, Riccardo, et al.
Published: (2026)

A note on spatially inhomogeneous Cahn-Hilliard energies
by: Wojtowytsch, Stephan
Published: (2024)

Uniqueness and regularity for the Navier-Stokes-Cahn-Hilliard system
by: Giorgini, Andrea, et al.
Published: (2018)

Interface dynamics in a degenerate Cahn-Hilliard model for viscoelastic phase separation
by: Hopf, Katharina, et al.
Published: (2024)

On a Cahn-Hilliard equation for the growth and division of chemically active droplets modeling protocells
by: Garcke, Harald, et al.
Published: (2025)

Nonnegative Weak Solution to the Degenerate Viscous Cahn-Hilliard Equation
by: Luong, Toai
Published: (2023)

Metastability and layer dynamics for the hyperbolic relaxation of the Cahn-Hilliard equation
by: Folino, Raffaele, et al.
Published: (2018)

Cahn-Hilliard Equations on Lattices: Dynamic Transitions and Pattern Formations
by: Grossman, Jared, et al.
Published: (2025)

On the Cahn-Hilliard equation with nonlinear diffusion: the non-convex case
by: Conti, Monica, et al.
Published: (2025)

Singularities in phase separation models: a spectral element approach for the nonlocal Cahn-Hilliard equation
by: Miniguano-Trujillo, Andrés, et al.
Published: (2026)

The linear Cahn-Hilliard equation with an interface
by: Chatziafratis, Andreas, et al.
Published: (2026)

Well-posedness of a bulk-surface convective Cahn--Hilliard system with dynamic boundary conditions
by: Knopf, Patrik, et al.
Published: (2024)

Volume Preserving Willmore Flow in a Generalized Cahn-Hilliard Flow
by: Chen, Yuan
Published: (2024)

On feedback stabilisation for the Cahn-Hilliard equation and its numerical approximation
by: Egger, Herbert, et al.
Published: (2025)

Structure-preserving approximation for the non-isothermal Cahn-Hilliard-Navier-Stokes system
by: Brunk, Aaron, et al.
Published: (2024)

On the uniqueness of strong solution to the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system
by: Jiang, Lingxin, et al.
Published: (2025)

The stochastic nonlocal Cahn-Hilliard equation with regular potential and multiplicative noise
by: Di Primio, Andrea, et al.
Published: (2026)

Well-posedness and long-time behavior of a bulk-surface Cahn--Hilliard model with non-degenerate mobility
by: Stange, Jonas
Published: (2025)

Viscoelastic Cahn--Hilliard models for tumour growth
by: Garcke, Harald, et al.
Published: (2022)

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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