Partial Differential Equations and Applications

2020 - 2025

Current editor(s): Zhitao Zhang

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Volume 4, issue 6, 2023

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

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

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

Volume 4, issue 5, 2023

Besov regularity of inhomogeneous parabolic PDEs pp. 1-61

Cornelia Schneider and Flóra Orsolya Szemenyei

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

A. V. da Silva

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

Yanheng Ding, Qi Guo and Yuanyang Yu

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

Michaël Ndjinga and Marcial Nguemfouo

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

Pascal Heid

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

Volume 4, issue 4, 2023

Nonlinear semigroups for nonlocal conservation laws pp. 1-26

Mihály Kovács and Mihály A. Vághy

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

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

Katrin Grunert and Audun Reigstad

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

Jiang Yu Nguwi and Nicolas Privault

Preface pp. 1-3

Marek Fila, Kazuhiro Ishige, Tohru Ozawa and Senjo Shimizu

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

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

Tanmay Sarkar

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

Karla Carolina V. de Sousa and Leandro S. Tavares

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

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

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

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

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

Volume 4, issue 3, 2023

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

Luis Espath

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

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

Ammar Khemmoudj

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

Keisuke Abiko

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

Vladimir Bobkov and Mieko Tanaka

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

Fayssal Djellali, Tijani A. Apalara and Mohamed Zitouni

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

Mourad Bellassoued and Mourad Choulli

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

Pascal Remy

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

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

Jason Minghan Dong

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

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

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

Alden Waters

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

Xiushuai Li and Jiao Jiang

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

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

On concentration in vortex sheets pp. 1-39

Samuel Lanthaler

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

Guy Fabrice Foghem Gounoue

Volume 4, issue 1, 2023

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

Leila Setayeshgar

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

Luis Espath

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

Young-Pil Choi