Partial Differential Equations and Applications

2020 - 2026

Current editor(s): Zhitao Zhang

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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

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

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

Volume 5, issue 5, 2024

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

Michael Gößwein, Matteo Novaga and Paola Pozzi

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

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

Andrea Mantile and Andrea Posilicano

Volume 5, issue 4, 2024

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

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

Katrin Grunert and Matthew Tandy

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

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

Mourad Choulli

Volume 5, issue 3, 2024

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

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

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

Pu-Zhao Kow and Henrik Shahgholian

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

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

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

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

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

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

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

David Arcoya, Francisco Odair Paiva and José M. Mendoza

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

Volume 4, issue 6, 2023

Solving stationary inverse heat conduction in a thin plate pp. 1-26

Jennifer Chepkorir, Fredrik Berntsson and Vladimir Kozlov

Sharp well-posedness of the biharmonic Schrödinger equation in a quarter plane pp. 1-25

E. Compaan and N. Tzirakis

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions pp. 1-51

Victor Boussange, Sebastian Becker, Arnulf Jentzen, Benno Kuckuck and Loïc Pellissier

Combining the hybrid mimetic mixed method with the Scharfetter-Gummel scheme for magnetised transport in plasmas pp. 1-27

Hanz Martin Cheng, Jan ten Thije Boonkkamp, Jesper Janssen, Diana Mihailova and Jan van Dijk

Stochastic evolution equations with rough boundary noise pp. 1-27

Alexandra Neamţu and Tim Seitz

Dirac cohomology on manifolds with boundary and spectral lower bounds pp. 1-36

Simone Farinelli

Volume 4, issue 5, 2023

Well posedness for the Poisson problem on closed Lipschitz manifolds pp. 1-19

Michaël Ndjinga and Marcial Nguemfouo

On the range of unsolvable systems induced by complex vector fields pp. 1-29

A. V. da Silva

Neural networks for first order HJB equations and application to front propagation with obstacle terms pp. 1-36

Olivier Bokanowski, Averil Prost and Xavier Warin

Besov regularity of inhomogeneous parabolic PDEs pp. 1-61

Cornelia Schneider and Flóra Orsolya Szemenyei

Semiclassical states of a type of Dirac–Klein–Gordon equations with nonlinear interacting terms pp. 1-26

Yanheng Ding, Qi Guo and Yuanyang Yu

A damped Kačanov scheme for the numerical solution of a relaxed p(x)-Poisson equation pp. 1-20

Pascal Heid

Volume 4, issue 4, 2023

Higher-order error estimates for physics-informed neural networks approximating the primitive equations pp. 1-35

Ruimeng Hu, Quyuan Lin, Alan Raydan and Sui Tang

Optimal error estimates of an IPDG scheme for the resistive magnetic induction equation pp. 1-33

Tanmay Sarkar

Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on $${{\mathbb {R}}}^3$$ R 3 subject to attractive background charges pp. 1-10

Raphael Winter

A deep learning approach to the probabilistic numerical solution of path-dependent partial differential equations pp. 1-20

Jiang Yu Nguwi and Nicolas Privault

Nonlinear semigroups for nonlocal conservation laws pp. 1-26

Mihály Kovács and Mihály A. Vághy

On an indefinite nonhomogeneous equation with critical exponential growth pp. 1-12

Karla Carolina V. de Sousa and Leandro S. Tavares

Choquard equations with mixed potential pp. 1-18

Romildo N. Lima and Marco A. S. Souto

Energy equality of MHD system under a weaker condition on magnetic field pp. 1-18

Taichi Eguchi

A regularized system for the nonlinear variational wave equation pp. 1-71

Katrin Grunert and Audun Reigstad

Asymptotics of solutions for the fractional modified Korteweg–de Vries equation of order $$\alpha \in \left( 2,3\right) $$ α ∈ 2, 3 pp. 1-15

Rafael Carreño-Bolaños, Nakao Hayashi and Pavel I. Naumkin

Sparse grid time-discontinuous Galerkin method with streamline diffusion for transport equations pp. 1-25

Andreas Zeiser

Fourth-order nonlinear degenerate problem for image decomposition pp. 1-25

Ahmed Nokrane, Nour Eddine Alaa and Fatima Aqel

Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus pp. 1-31

Akihiko Takahashi and Toshihiro Yamada

Preface pp. 1-3

Marek Fila, Kazuhiro Ishige, Tohru Ozawa and Senjo Shimizu

On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam pp. 1-14

Paulo Amorim, João-Paulo Dias and Assis F. Martins

Volume 4, issue 3, 2023

General decay of the solution to a nonlinear viscoelastic beam with delay pp. 1-25

Ammar Khemmoudj

On the antimaximum principle for the p-Laplacian and its sublinear perturbations pp. 1-38

Vladimir Bobkov and Mieko Tanaka

Gevrey regularity of the solutions of some inhomogeneous semilinear partial differential equations with variable coefficients pp. 1-18

Pascal Remy

Phragmén–Lindelöf theorems for a weakly elliptic equation with a nonlinear dynamical boundary condition pp. 1-13

Keisuke Abiko

Existence of solutions for resonant double phase problems with mixed boundary value conditions pp. 1-17

Yihao Yang, Wulong Liu, Patrick Winkert and Xingye Yan

Global logarithmic stability of a Cauchy problem for anisotropic wave equations pp. 1-44

Mourad Bellassoued and Mourad Choulli

Uniform stability of a thermodiffusion Timoshenko beam pp. 1-20

Fayssal Djellali, Tijani A. Apalara and Mohamed Zitouni

Correction to: A continuum framework for phase field with bulk-surface dynamics pp. 1-1

Luis Espath

Volume 4, issue 2, 2023

Mittag-leffler-type function of arbitrary order and their application in the fractional kinetic equation pp. 1-25

M. A. Pathan and Maged G. Bin-Saad

Well-posedness for the initial value problem associated to the Zakharov–Kuznetsov (ZK) equation in asymmetric spaces pp. 1-12

Émile Deléage and Felipe Linares

Topological approaches to knotted electric charge distributions pp. 1-12

Max Lipton

Solution curve for linear control systems on Lie groups pp. 1-18

João Paulo Lima de Oliveira, Alexandre J. Santana and Simão N. Stelmastchuk

Stability of neutral Volterra integro-differential equations with infinite delay pp. 1-7

Xiushuai Li and Jiao Jiang

On rotational surfaces with circular boundary and almost constant mean curvature pp. 1-6

Jason Minghan Dong

A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces pp. 1-36

Guy Fabrice Foghem Gounoue

Local bounds of the gradient of weak solutions to the porous medium equation pp. 1-35

Ugo Gianazza and Juhana Siljander

Existence and uniqueness of solution for some time fractional parabolic equations involving the 1-Laplace operator pp. 1-35

Claudianor O. Alves and Tahir Boudjeriou

Observability for Schrödinger equations with quadratic Hamiltonians pp. 1-33

Alden Waters

On concentration in vortex sheets pp. 1-39

Samuel Lanthaler

Some maximum principles for the drift Laplacian applied to complete spacelike hypersurfaces pp. 1-16

Danilo F. Silva, Eraldo A. Lima and Henrique F. Lima

An energy-based deep splitting method for the nonlinear filtering problem pp. 1-27

Kasper Bågmark, Adam Andersson and Stig Larsson

Volume 4, issue 1, 2023

On the rigorous derivation of hydrodynamics of the Kuramoto model for synchronization phenomena pp. 1-20

Young-Pil Choi

A continuum framework for phase field with bulk-surface dynamics pp. 1-17

Luis Espath

Uniform large deviations for a class of semilinear stochastic partial differential equations driven by a Brownian sheet pp. 1-12

Leila Setayeshgar