Partial Differential Equations and Applications

2020 - 2025

Current editor(s): Zhitao Zhang

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Volume 6, issue 6, 2025

Stability and large-time behavior for the 2D Boussinesq system with vertical dissipation and horizontal thermal diffusion pp. 1-44

Oussama Ben Said and Mona Ben Said

Classical solutions for a class of Euler equations of ideal gas dynamics pp. 1-13

Svetlin G. Georgiev and Gal Davidi

Skyrmions in two dimensional cholesteric liquid crystals pp. 1-21

Carlo Greco

Sign-changing solutions for a perturbed biharmonic equation with critical exponent pp. 1-21

Rabeh Ghoudi and Moufida Lahrach

Horizontal harmonic maps between finsler manifolds pp. 1-22

Qun Chen and Haowei Lin

Global analytic solution to the IVP for the BBM equation posed on $$\mathbb {R}$$ R and $$\mathbb {T}$$ T pp. 1-26

Mikaela Baldasso and Mahendra Panthee

Volume 6, issue 5, 2025

Gradient regularity for widely degenerate elliptic partial differential equations pp. 1-51

Michael Strunk

On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule pp. 1-42

Scipio Cuccagna and Masaya Maeda

Existence of ground state solutions for the critical case of Berestycki-Lions’ theorem pp. 1-26

Shinji Adachi and Tatsuya Watanabe

Large time asymptotics for the fractional Schrödinger equation with subcritical derivative nonlinearities pp. 1-22

Nakao Hayashi and Pavel I. Naumkin

Volume 6, issue 4, 2025

Multiplicity results for a nonlocal system with critical growth pp. 1-15

Jeziel N. Correia and Claudionei P. Oliveira

On the regularity of Dirac eigenfunctions pp. 1-18

Tuyen Vu

New results for a class of quasilinear Schrödinger equations pp. 1-18

Taib Talbi

Speckle noise removal in color images using a generalized nonstandard fourth-order variational method pp. 1-30

Badreddine Rjaibi and Didier Auroux

Correction to “The unique continuation property for second order evolution PDEs” [Partial Differ. Equ. Appl. 2, 67 (2021), 46 p] with additional comments pp. 1-8

Mourad Choulli

Existence and uniqueness of large solutions of a degenerate and/or singular semilinear elliptic problem pp. 1-17

Raj Narayan Dhara

Partial classification of the large-time behavior of solutions to cubic nonlinear Schrödinger systems pp. 1-52

Satoshi Masaki

Local and global solutions to Stokes-Magneto equations with fractional dissipations pp. 1-23

Hantaek Bae, Hyunwoo Kwon and Jaeyong Shin

Fractional Sobolev spaces for the singular-perturbed Laplace operator in the $$L^p$$ L p setting pp. 1-40

Vladimir Georgiev and Mario Rastrelli

On Schrödinger equation with square and inverse-square potentials pp. 1-11

Atsuhide Ishida and Masaki Kawamoto

Volume 6, issue 3, 2025

Asymptotic behavior for the dissipative nonlinear Schrödinger equations under mass supercritical setting pp. 1-14

Gaku Hoshino

Multiplicity of solutions for a nonlinear Schrödinger system with three wave interaction pp. 1-14

Tomoharu Kinoshita and Yuki Osada

The existence of $$L^2$$ L 2 -constrained solutions for Kirchhoff equations with $$L^2$$ L 2 -critical general nonlinearity pp. 1-25

Hongyu Ye and Jiahui Yin

Bifurcations and dynamical behaviors for a generalized Maginu model with distributed delay pp. 1-24

Xiaowei Ju

Classification of weak and unbounded traveling wave solutions for a Porous–Fisher-KPP equation pp. 1-24

Yu Ichida

On the well-posedness of the periodic fractional Schrödinger equation pp. 1-28

Beckett Sanchez, Oscar Riaño and Svetlana Roudenko

Longtime behavior of a free boundary model with nonlocal diffusion in online social networks pp. 1-26

Phuong Le

A zero-sum differential game for two opponent masses pp. 1-23

Fabio Bagagiolo, Rossana Capuani and Luciano Marzufero

Volume 6, issue 2, 2025

Multiple solutions for superlinear fractional p-Laplacian equations pp. 1-20

Antonio Iannizzotto, Vasile Staicu and Vincenzo Vespri

On the sharp constants in the regional fractional Sobolev inequalities pp. 1-20

Rupert L. Frank, Tianling Jin and Wei Wang

Adaptive sensitivity control for a feedback loop and a consensus model with unknown delay pp. 1-20

Jan Haskovec

Regular solution to hyperbolic boundary value problems without regularization pp. 1-38

Antoine Benoit

Convergence of one-dimensional stationary mean field games with vanishing potential pp. 1-16

Yiru Cai, Haobo Qi, Xifeng Su and Yi Tan

Degenerate free boundary problems with oscillatory singularities pp. 1-16

Aelson Sobral, Eduardo V. Teixeira and José Miguel Urbano

A second-order Mean Field Games model with controlled diffusion pp. 1-34

Vincenzo Ignazio and Michele Ricciardi

Norm inflation for a higher-order nonlinear Schrödinger equation with a derivative on the circle pp. 1-14

Toshiki Kondo and Mamoru Okamoto

Volume 6, issue 1, 2025

Axially symmetric Willmore minimizers with prescribed isoperimetric ratio pp. 1-60

Jan-Henrik Metsch

Modeling and mathematical analysis of the clogging phenomenon in filtration filters installed in aquaria pp. 1-71

Ken Furukawa and Hiroyuki Kitahata

Vlasov equations on directed hypergraph measures pp. 1-49

Christian Kuehn and Chuang Xu

Instability of stationary solutions for double power nonlinear Schrödinger equations in one dimension pp. 1-23

Noriyoshi Fukaya and Masayuki Hayashi

A uniqueness result for the d-dimensional magnetohydrodynamics equations with fractional dissipation in Besov spaces pp. 1-27

Hua Qiu, Xia Wang and Zheng-an Yao

A construction of peak solutions by a local mountain pass approach for a nonlinear Schrödinger system with three wave interaction pp. 1-26

Yuki Osada and Yohei Sato

Singular elliptic PDEs: an extensive overview pp. 1-82

Francescantonio Oliva and Francesco Petitta

On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis pp. 1-31

Simone Fagioli, Emanuela Radici and Licia Romagnoli

Existence and stability of near-constant solutions of variable-coefficient scalar field equations pp. 1-28

Mashael Alammari and Stanley Snelson

Volume 5, issue 6, 2024

Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations pp. 1-47

Christian Beck, Lukas Gonon and Arnulf Jentzen

Travelling waves for discrete stochastic bistable equations pp. 1-23

Carina Geldhauser and Christian Kuehn

Solvability of a semilinear parabolic equation on Riemannian manifolds pp. 1-22

Xinran Wei and Mengmeng Zhang

Non linear singular drifts and fractional operators pp. 1-39

Diego Chamorro and Stéphane Menozzi

Regularizing effect of lower order terms in nonlinear Dirichlet problems with singularity pp. 1-19

Abdelaaziz Sbai, Youssef El Hadfi and Mounim El Ouardy

Volume 5, issue 5, 2024

New instability, blow-up and break-down effects for Sobolev-type evolution PDE: asymptotic analysis for a celebrated pseudo-parabolic model on the quarter-plane pp. 1-45

Andreas Chatziafratis and Tohru Ozawa

Remark on the uniqueness of the mild solution of SQG equation pp. 1-9

Tsukasa Iwabuchi and Ryoma Ueda

Stability analysis for the anisotropic curve shortening flow of planar networks pp. 1-42

Michael Gößwein, Matteo Novaga and Paola Pozzi

The point scatterer approximation for wave dynamics pp. 1-30

Andrea Mantile and Andrea Posilicano

Positive solutions of nonlinear elliptic equations involving unbounded variable exponents and convection term pp. 1-15

Anderson Araujo, Luiz Faria and Dumitru Motreanu

Volume 5, issue 4, 2024

Parameter analysis in continuous data assimilation for three-dimensional Brinkman–Forchheimer-extended Darcy model pp. 1-32

Débora A. F. Albanez and Maicon José Benvenutti

Global weak solutions to a phase-field model for seawater solidification with melt convection pp. 1-17

Md Akram Hossain and Li Ma

On global $$W^{2,\delta }$$ W 2, δ estimates for the Monge–Ampère equation on general bounded convex domains pp. 1-10

Nam Q. Le

Notes on asymptotic behavior of radial solutions for some weighted elliptic equations on the annulus pp. 1-15

Futoshi Takahashi

Uniqueness of continuation for semilinear elliptic equations pp. 1-14

Mourad Choulli

A Lipschitz metric for $$\alpha $$ α -dissipative solutions to the Hunter–Saxton equation pp. 1-33

Katrin Grunert and Matthew Tandy

Volume 5, issue 3, 2024

Bifurcations and dynamical behaviors for a generalized delayed-diffusive Maginu model pp. 1-21

Xiaowei Ju

Global $$L^\infty $$ L ∞ -estimate for general quasilinear elliptic equations in arbitrary domains of $${{\mathbb {R}}}^N$$ R N pp. 1-15

Siegfried Carl and Hossein Tehrani

On the existence, regularity and uniqueness of $$L^p$$ L p -solutions to the steady-state 3D Boussinesq system in the whole space and with gravity acceleration pp. 1-30

Oscar Jarrín

On local decay of inflaton and axion fields pp. 1-30

Matías Morales and Claudio Muñoz

Multi-phase k-quadrature domains and applications to acoustic waves and magnetic fields pp. 1-28

Pu-Zhao Kow and Henrik Shahgholian

Existence of positive solutions for a p-Schrödinger–Kirchhoff integro-differential equation with critical growth pp. 1-31

Juan Mayorga-Zambrano and Henry Cumbal-López

Cancellation properties and unconditional well-posedness for the fifth order KdV type equations with periodic boundary condition pp. 1-55

Takamori Kato and Kotaro Tsugawa

Two-scale convergence of a class of r-forms: rewriting of periodic homogenization of Maxwell’s equations pp. 1-29

Alphonse Mba, Marcial Nguemfouo and Hubert Nnang

Continuity estimates for Riesz potentials on polygonal boundaries pp. 1-20

Xavier Claeys, Muhammad Hassan and Benjamin Stamm

An MP-Newton method for finding orthogonal-max type critical points and its application for calculating multiple solutions of semilinear elliptic equations: part I—method pp. 1-26

Xudong Yao

Volume 5, issue 2, 2024

Energy decay analysis for Porous elastic system with microtemperature: Classical vs second spectrum approach pp. 1-28

Hamza Zougheib, Toufic El Arwadi, Mohammad El-Hindi and Abdelaziz Soufyane

Scattering problems for the wave equation in 1D: D’Alembert-type representations and a reconstruction method pp. 1-25

Konstantinos Kalimeris and Leonidas Mindrinos

Existence and multiplicity of solutions for a locally coercive elliptic equation pp. 1-15

David Arcoya, Francisco Odair Paiva and José M. Mendoza

Spectral inequality with sensor sets of decaying density for Schrödinger operators with power growth potentials pp. 1-18

Alexander Dicke, Albrecht Seelmann and Ivan Veselić

Existence of solutions for superquadratic or asymptotically quadratic fractional Hamiltonian systems pp. 1-19

Mohsen Timoumi

Volume 5, issue 1, 2024

Hamilton and Li–Yau type gradient estimates for a weighted nonlinear parabolic equation under a super Perelman–Ricci flow pp. 1-38

Ali Taheri and Vahideh Vahidifar

Hyper-reduction for parametrized transport dominated problems via adaptive reduced meshes pp. 1-19

Sara Grundel and Neeraj Sarna

Global dynamics below a threshold for the nonlinear Schrödinger equations with the Kirchhoff boundary and the repulsive Dirac delta boundary on a star graph pp. 1-36

Masaru Hamano, Masahiro Ikeda, Takahisa Inui and Ikkei Shimizu

Uniform convergence for linear elastostatic systems with periodic high contrast inclusions pp. 1-39

Xin Fu and Wenjia Jing