Partial Differential Equations and Applications

2020 - 2025

Current editor(s): Zhitao Zhang

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Volume 6, issue 3, 2025

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

Gaku Hoshino

Volume 6, issue 2, 2025

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

Toshiki Kondo and Mamoru Okamoto

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

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

Vincenzo Ignazio and Michele Ricciardi

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

Volume 6, issue 1, 2025

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

Francescantonio Oliva and Francesco Petitta

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

Ken Furukawa and Hiroyuki Kitahata

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

Mashael Alammari and Stanley Snelson

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

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

Vlasov equations on directed hypergraph measures pp. 1-49

Christian Kuehn and Chuang Xu

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

Simone Fagioli, Emanuela Radici and Licia Romagnoli

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

Noriyoshi Fukaya and Masayuki Hayashi

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

Jan-Henrik Metsch

Volume 5, issue 6, 2024

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

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

Carina Geldhauser and Christian Kuehn

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

Abdelaaziz Sbai, Youssef El Hadfi and Mounim El Ouardy

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

Volume 5, issue 5, 2024

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

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

Volume 5, issue 4, 2024

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

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

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

Volume 5, issue 3, 2024

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

Xavier Claeys, Muhammad Hassan and Benjamin Stamm

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

Xiaowei Ju

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

Pu-Zhao Kow and Henrik Shahgholian

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

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

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

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

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

Volume 5, issue 2, 2024

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

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

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

David Arcoya, Francisco Odair Paiva and José M. Mendoza

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 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

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

Xin Fu and Wenjia Jing

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