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Bibliographic Details
Main Author:	Pawlak, Karolina
Format:	Preprint
Published:	2025
Subjects:	Analysis of PDEs 35R11, 47G40, 35R37
Online Access:	https://arxiv.org/abs/2506.15356
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Large time behaviour of the fractional heat equation associated with the Dunkl Laplacian
by: Mukherjee, Suman
Published: (2026)

Local uniqueness of multi-peak positive solutions to a class of fractional Kirchhoff equations
by: Yang, Zhipeng
Published: (2022)

Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation
by: Ahmad, Sofwah, et al.
Published: (2025)

Regularity for mixed-order nonlinear fractional equations with degenerate coefficients
by: Lee, Ho-Sik, et al.
Published: (2025)

On a fractional Alt-Caffarelli-Friedman-type monotonicity formula
by: Ferrari, Fausto, et al.
Published: (2025)

Boundary regularity for general elliptic operators of order $2s$
by: Grube, Florian, et al.
Published: (2026)

Critical fractional Kirchhoff problems: Uniqueness and Nondegeneracy
by: Yang, Zhipeng, et al.
Published: (2025)

Existence and regularity results for space-time fractional integro-differential equation of Kirchhoff type with memory
by: Kumar, Lalit, et al.
Published: (2024)

Fine boundary regularity for the singular fractional p-Laplacian
by: Iannizzotto, Antonio, et al.
Published: (2024)

Nonlocal equations with kernels of general order
by: Ok, Jihoon, et al.
Published: (2025)

Supercritical Schrödinger equations involving integro-differential operators and vanishing potentials
by: Duarte, Ronaldo C., et al.
Published: (2026)

Existence results for Cahn-Hilliard type systems driven by nonlocal integrodifferential operators with singular kernels
by: Davoli, Elisa, et al.
Published: (2024)

Fractional elliptic reaction-diffusion systems with coupled gradient terms and different diffusion
by: Atmani, Somia, et al.
Published: (2025)

Liouville type theorems for dual nonlocal evolution equations involving Marchaud derivatives
by: Guo, Yahong, et al.
Published: (2024)

Logarithmic convexity of non-symmetric time-fractional diffusion equations
by: Chorfi, S. E., et al.
Published: (2024)

Density estimates for a nonlocal variational model with a degenerate double-well potential via the Sobolev inequality
by: Dipierro, Serena, et al.
Published: (2025)

Symmetry and monotonicity of singular solutions for the Hartree equation
by: Cai, Ying, et al.
Published: (2025)

Anisotropic fractional Sobolev spaces with variable exponent and application to nonlocal problems
by: Azroul, Elhoussine, et al.
Published: (2024)

The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis
by: Dipierro, Serena, et al.
Published: (2024)

Boundedness estimates for nonlinear nonlocal kinetic Kolmogorov-Fokker-Planck equations
by: Anceschi, Francesca, et al.
Published: (2023)

Properties of fractional p-Laplace equations with sign-changing potential
by: Duan, Yubo, et al.
Published: (2024)

On a doubly sublinear fractional $p$-Laplacian equation
by: Iannizzotto, A., et al.
Published: (2024)

Fujita exponent for the fractional sub-Laplace semilinear heat equation with forcing term on the Heisenberg group
by: Oza, Priyank, et al.
Published: (2025)

Tools for stability analysis of fractional reaction diffusion systems
by: Ahmad, Sofwah, et al.
Published: (2025)

Direct and inverse source problems for two-term time-fractional diffusion equation with Hilfer derivative
by: Salakhitdinov, M. S., et al.
Published: (2017)

Gradient Flow Solutions For Porous Medium Equations with Nonlocal Lévy-type Pressure
by: Foghem, Guy, et al.
Published: (2023)

Fractional Morrey-Sobolev type embeddings and nonlocal subelliptic problems with oscillating nonlinearities on stratified Lie groups
by: Ghosh, Sekhar, et al.
Published: (2025)

Propagating front solutions in a time-fractional Fisher-KPP equation
by: Ishii, Hiroshi
Published: (2023)

The time-fractional Airy equation on the metric graphs
by: Kamoladdin, Rakhimov, et al.
Published: (2026)

Gradual smoothing: strong hypercontractivity and logarithmic Sobolev inequalities
by: de Pablo, Arturo, et al.
Published: (2026)

Positivity and asymptotic behaviour of solutions to a generalized nonlocal fast diffusion equation
by: de Pablo, Arturo, et al.
Published: (2024)

An effective advection induced by oscillating microstructure in a diffusion equation
by: Wiedemann, David
Published: (2024)

A Calderón type inverse problem for the active scalar equations with fractional dissipation
by: Li, Li, et al.
Published: (2024)

Inverse source problem for the space-time fractional parabolic equation on a metric star graph with an integral overdetermination condition
by: Ashurov, R. R., et al.
Published: (2024)

Master equations with indefinite nonlinearities
by: Chen, Wenxiong, et al.
Published: (2024)

Inverse problem for a multi-term time-fractional diffusion equation with the Caputo derivatives
by: Ashurov, Ravshan, et al.
Published: (2026)

$L_p$-estimates for nonlocal equations with general Lévy measures
by: Dong, Hongjie, et al.
Published: (2025)

Local multiplicity for fractional linear equations with Hardy potentials
by: Mainini, Edoardo, et al.
Published: (2024)

Nonlocal equations with gradient constraints
by: Safdari, Mohammad
Published: (2021)

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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