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Bibliographic Details
Main Authors:	Bazhlekov, Ivan, Bazhlekova, Emilia
Format:	Preprint
Published:	2025
Subjects:	Analysis of PDEs Mathematical Physics
Online Access:	https://arxiv.org/abs/2512.09426
Tags:	Add Tag No Tags, Be the first to tag this record!

Estimating parameters of the diffusion model via asymptotic expansions
by: Kalimeris, Konstantinos, et al.
Published: (2025)

Practical tensor calculus on embedded submanifolds of arbitrary codimension
by: Yushutin, Vladimir
Published: (2026)

Reaction-diffusion systems from kinetic models for bacterial communities on a leaf surface
by: Bisi, Marzia, et al.
Published: (2025)

Self-consistent equations and quantum diffusion for the Anderson model
by: Black, Adam, et al.
Published: (2025)

On anomalous diffusion in the Kraichnan model and correlated-in-time variants
by: Rowan, Keefer
Published: (2023)

A variational approach to the modeling of compressible magnetoelastic materials
by: Benešová, Barbora, et al.
Published: (2024)

A micro-scale diffused interface model with Flory-Huggins logarithmic potential in a porous medium
by: Lakhmara, Nitu, et al.
Published: (2023)

On clogged and fast diffusions in porous media with fractional pressure
by: de Courcel, Antonin Chodron
Published: (2025)

Nonlinear diffusion limit of non-local interactions on a sphere
by: Peletier, Mark A., et al.
Published: (2025)

On the diffusion approximation of the stationary radiative transfer equation with absorption and emission
by: Demattè, Elena, et al.
Published: (2023)

Lie symmetry method for a nonlinear heat-diffusion equation
by: Bollati, Julieta, et al.
Published: (2026)

Fractional Ito Calculus for Randomly Scaled Fractional Brownian Motion and its Applications to Evolution Equations
by: Butko, Yana A., et al.
Published: (2024)

Turing pattern induced by cross-diffusion in cancer immunotherapy model
by: Munafò, C. F., et al.
Published: (2025)

Inverse problem for the abstract diffusion-wave equation with Caputo fractional derivative
by: Durdiev, D. K., et al.
Published: (2025)

Inverse coefficient problems for one-dimensional time-fractional diffusion equations
by: Imanuvilov, Oleg, et al.
Published: (2024)

Higher-order diffusion and Cahn-Hilliard-type models revisited on the half-line
by: Chatziafratis, A., et al.
Published: (2025)

Solutions of time fractional anomalous diffusion equations with coefficients depending on both time and space variables
by: Bat-Ochir, Ganbileg, et al.
Published: (2024)

Notes on an intuitive approach to elliptic homogenization
by: Rowan, Conor
Published: (2026)

Inverse problem of determining the right-hand side of a one-dimensional fractional diffusion equation with variable coefficients
by: Durdiev, D. K.
Published: (2024)

Wigner measure approach to the derivation of the Landau-Pekar equations in the mean-field limit
by: Gautier, Raphaël
Published: (2025)

Wave propagation for 1-dimensional reaction-diffusion equations with nonzero random drift
by: Guan, Dihang, et al.
Published: (2025)

A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds
by: Bulut, Aynur, et al.
Published: (2020)

Stochastic Fractional Navier-Stokes Equations: Finite-Time Blow-up for Vortex Stretch Singularities
by: Saucedo, Joel, et al.
Published: (2025)

Mean field limits of particle-based stochastic reaction-drift-diffusion models
by: Heldman, Max, et al.
Published: (2023)

On Bourgain's approach to stochastic homogenization
by: Duerinckx, Mitia, et al.
Published: (2024)

Conditional well-posedness and data-driven method for identifying the dynamic source in a coupled diffusion system from one single boundary measurement
by: Sun, Chunlong, et al.
Published: (2024)

Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians
by: Hake, Philipp, et al.
Published: (2026)

Robust series linearization of nonlinear advection-diffusion equations
by: Kieffer, T. Forrest, et al.
Published: (2025)

Nonlinear Kirchhoff-Love shell models derived from the Ciarlet-Geymonat energy: modelling and well-posedness
by: Ghiba, Ionel-Dumitrel, et al.
Published: (2026)

An eigensystem approach to Anderson localization for multi-particle systems
by: Bringmann, Bjoern, et al.
Published: (2020)

Asymptotic models for the evolution of a circular biofilm
by: Alonso-Orán, Diego, et al.
Published: (2025)

Singularity formation for the higher dimensional Skyrme model
by: McNulty, Michael
Published: (2024)

On a repulsion model with Coulomb interaction and nonlinear mobility
by: de Courcel, Antonin Chodron, et al.
Published: (2025)

About a nonideal Rayleigh gas mixture model
by: Fougères, Florent
Published: (2026)

A viscoelastic model for skin via homogenization theory
by: Casado-Díaz, Juan
Published: (2024)

On an inhomogeneous coagulation model with a differential sedimentation kernel
by: Cristian, Iulia, et al.
Published: (2024)

Cumulants of the Rayleigh gas mixture model: statistical results
by: Fougères, Florent
Published: (2026)

On the steadiness of symmetric solutions to two dimensional dispersive models
by: Pei, Long, et al.
Published: (2024)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// 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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