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Main Author:	Boutillon, Nathanaël
Format:	Preprint
Published:	2022
Subjects:	Analysis of PDEs 35K57 (Primary), 35B40, 60F10 (Secondary)
Online Access:	https://arxiv.org/abs/2204.06593
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Long-time behavior for systems of Fisher-KPP type with interacting components
by: Stavrianidi, Alexandra
Published: (2026)

Reaction-diffusion model for a population structured in phenotype and space I -- Criterion for persistence
by: Boutillon, Nathanaël, et al.
Published: (2024)

Large deviations principle for the cubic NLS equation with slowly decaying data
by: Liang, Rui, et al.
Published: (2025)

Impact of diffusion mechanisms on persistence and spreading
by: Boutillon, Nathanaël, et al.
Published: (2025)

Fully nonlinear parabolic fixed transmission problems
by: Jesus, David, et al.
Published: (2025)

Global behavior of nonlocal in time reaction-diffusion equations
by: Torebek, Berikbol T.
Published: (2023)

Large Deviations for Stochastic Evolution Equations in the Critical Variational Setting
by: Theewis, Esmée, et al.
Published: (2024)

Asymptotics and periodic dynamics in a negative chemotaxis system with cell lethality
by: Herrero-Hervás, Federico, et al.
Published: (2025)

The influence of advection on the propagation phenomena of reaction-diffusion equations with KPP-bistable nonlinearity
by: Liang, Xing, et al.
Published: (2024)

Time Asymptotics and Scaling Limits for a Nonlocal Fokker-Planck Equation with Heavy-Tailed Kernel
by: Tassi, Niccolò
Published: (2026)

The principal eigenvalue problem for a strongly anisotropic second-order elliptic operator
by: Boutillon, Nathanaël
Published: (2023)

Quenching time and probability estimates for a stochastic reaction-diffusion system with coupled inner singular absorption terms driven by mixed noises
by: Kavallaris, Nikos I., et al.
Published: (2025)

Existence and Spatial Decay of Forced Waves for the Fisher-KPP Equation with a Degenerate Shifting Environment
by: Tang, Zhibao, et al.
Published: (2026)

Kermack-McKendrick type models for epidemics with nonlocal aggregation terms
by: Di Francesco, Marco, et al.
Published: (2024)

A Central Limit Theorem for Modified Massive Arratia Flow
by: Dorogovtsev, Andrey, et al.
Published: (2024)

Convergence and front position for an FKPP-type free boundary problem
by: Berestycki, Julien, et al.
Published: (2025)

Global dynamics for the energy-critical nonlinear heat equation
by: Ikeda, Masahiro, et al.
Published: (2024)

Nonlinear dynamics of reaction-diffusion wave trains under large and fully nonlocalized modulations
by: Alexopoulos, Joannis, et al.
Published: (2025)

Large deviations for an obstacle problem with T-monotone operator and multiplicative noise
by: Tahraoui, Yassine
Published: (2023)

A uniform-in-time nonlocal approximation of the standard Fokker-Planck equation
by: Cañizo, José A., et al.
Published: (2024)

Exponential equilibration of an electro-energy-reaction-diffusion system arising from a two-level semiconductor model
by: Kniely, Michael
Published: (2025)

Optimizing Resource Distribution in a One-Dimensional Logistic Diffusion Model
by: Heo, Junyoung, et al.
Published: (2025)

On well-posedness for second-order degenerate parabolic equations with unbounded lower-order terms
by: Baadi, Khalid
Published: (2025)

Interaction between initial behavior of temperature and the mean curvature of the interface in two-phase heat conductors
by: Sakaguchi, Shigeru
Published: (2024)

Chaos expansion solutions of a class of magnetic Schrödinger Wick-type stochastic equations on $\mathbb{R}^d$
by: Coriasco, Sandro, et al.
Published: (2023)

On local energy decay for solutions to the b-family of peakon equations
by: Hong, Christian
Published: (2024)

Orbital stability of plane waves in the Klein-Gordon equation against localized perturbations
by: Bukieda, Emile, et al.
Published: (2025)

Asymptotically self-similar global solutions for Hardy-Hénon parabolic equations
by: Chikami, Noboru, et al.
Published: (2025)

Quantitative stability for quasilinear parabolic equations
by: Kurkinen, Tapio, et al.
Published: (2026)

Generalized solutions to hyperbolic systems with random field coefficients
by: Karakašević, Jelena, et al.
Published: (2024)

Coupled reaction-diffusion equations on adjacent domains
by: Berestycki, Henri, et al.
Published: (2019)

Optimal regularity for degenerate parabolic equations on a flat boundary
by: Yun, Hyungsung
Published: (2025)

Uniqueness and root-Lipschitz regularity for a degenerate heat equation
by: Dunlap, Alexander, et al.
Published: (2023)

Identification of the Heat Transfer Coefficient Using an Inverse Heat Conduction Model
by: Pyatkov, Sergey Grigorievich
Published: (2024)

On a class of triangular cross-diffusion systems and its fast reaction approximation
by: Brocchieri, Elisabetta, et al.
Published: (2025)

Exceptional Boundary Sets for Solutions of Fully Nonlinear Parabolic PDEs
by: Verma, Ram Baran, et al.
Published: (2024)

Parabolic boundary Harnack inequalities with right-hand side
by: Torres-Latorre, Clara
Published: (2023)

Regularity theory for fully nonlinear equations of porous medium-type
by: Yun, Hyungsung
Published: (2024)

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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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