Partial Differential Equations and Applications

2020 - 2025

Current editor(s): Zhitao Zhang

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Volume 2, issue 6, 2021

Local gradient estimates for second-order nonlinear elliptic and parabolic equations by the weak Bernstein’s method pp. 1-15

G. Barles

On a Navier–Stokes–Ohm problem from plasma physics in multi connected domains pp. 1-18

Senjo Shimizu and Hidenobu Tsuritani

Inhomogeneous Dirichlet boundary value problem for nonlinear Schrödinger equations in the upper half-space pp. 1-24

Nakao Hayashi, Elena I. Kaikina and Takayoshi Ogawa

One-dimensional symmetry of positive bounded solutions to the nonlinear Schrödinger equation in the half-space in two and three dimensions pp. 1-6

Christos Sourdis

Elliptic problems in the half-space with nonlinear critical boundary conditions pp. 1-16

Marcelo Fernandes Furtado and Karla Carolina Vicente de Sousa

Hölder gradient estimates on $$L^p$$ L p -viscosity solutions of fully nonlinear parabolic equations with VMO coefficients pp. 1-22

Shota Tateyama

Mass-concentration of low-regularity blow-up solutions to the focusing 2D modified Zakharov–Kuznetsov equation pp. 1-29

Debdeep Bhattacharya

Note on smoothing estimates for Kolmogorov type equations pp. 1-12

Yasunori Maekawa

Optimal design of optical analog solvers of linear systems pp. 1-19

Kthim Imeri

On vanishing and localizing around corners of electromagnetic transmission resonances pp. 1-20

Huaian Diao, Hongyu Liu, Xianchao Wang and Ke Yang

A note on 2D Navier–Stokes equations pp. 1-3

Jishan Fan and Tohru Ozawa

Development and analysis of entropy stable no-slip wall boundary conditions for the Eulerian model for viscous and heat conducting compressible flows pp. 1-27

Mohammed Sayyari, Lisandro Dalcin and Matteo Parsani

On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations pp. 1-26

Hendrik Ranocha, Manuel Quezada Luna and David I. Ketcheson

Evolving to non-round Weingarten spheres: integer linear Hopf flows pp. 1-26

Brendan Guilfoyle and Wilhelm Klingenberg

Multilevel Picard iterations for solving smooth semilinear parabolic heat equations pp. 1-31

Weinan E, Martin Hutzenthaler, Arnulf Jentzen and Thomas Kruse

Multiple solutions for a class of fractional logarithmic Schrödinger equations pp. 1-30

Siyuan He and Xiaochun Liu

Volume 2, issue 5, 2021

Global well-posedness for the fractional Boussinesq–Coriolis system with stratification in a framework of Fourier–Besov type pp. 1-18

Leithold L. Aurazo-Alvarez and Lucas C. F. Ferreira

On the mathematical analysis of the artificial compressibility method pp. 1-19

Yoshiyuki Kagei

Traveling waves for the nonlinear variational wave equation pp. 1-21

Katrin Grunert and Audun Reigstad

The unique continuation property for second order evolution PDEs pp. 1-46

Mourad Choulli

A remark on the uniqueness of Kozono–Nakao’s mild $$L^3$$ L 3 -solutions on the whole time axis to the Navier–Stokes equations in unbounded domains pp. 1-16

Yasushi Taniuchi

High-dimensional distribution generation through deep neural networks pp. 1-44

Dmytro Perekrestenko, Léandre Eberhard and Helmut Bölcskei

Existence and upper semicontinuity of attractors for a class of non-Newtonian micropolar fluids pp. 1-24

M. M. Freitas, G. M. Araújo, F. D. M. Bezerra and M. A. F. Araújo

Lower bound estimate for the dissipative nonlinear Schrödinger equation pp. 1-11

Takuya Sato

Volume 2, issue 4, 2021

Modal approximation for plasmonic resonators in the time domain: the scalar case pp. 1-40

Lorenzo Baldassari, Pierre Millien and Alice L. Vanel

Optimal error estimate for a space-time discretization for incompressible generalized Newtonian fluids: the Dirichlet problem pp. 1-23

Luigi C. Berselli and Michael Růžička

Homogenization of the G-equation: a metric approach pp. 1-18

Antonio Siconolfi

Existence and concentration of solution for Schrödinger-Poisson system with local potential pp. 1-22

Zhipeng Yang and Yuanyang Yu

Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space pp. 1-48

Nikolas Nüsken and Lorenz Richter

Ultimate bound of solutions to second-order evolution equation with nonlinear damping term pp. 1-16

Faouzia Aloui

The Lie symmetry approach on (1+2)-dimensional financial models pp. 1-17

K. Charalambous, S. Kontogiorgis and C. Sophocleous

Stability and exact periodic solutions of indefinite equations arising from the Kepler problem on the sphere pp. 1-14

Xiaomeng Bo, Qihuai Liu and Wenye Liu

Breakdown of superconductivity in a magnetic field with self-intersecting zero set pp. 1-14

Kamel Attar

Transport and continuity equations with (very) rough noise pp. 1-26

C. Bellingeri, A. Djurdjevac, P. K. Friz and N. Tapia

Electromagnetic field enhancement in a subwavelength rectangular open cavity pp. 1-51

Yixian Gao, Peijun Li and Xiaokai Yuan

Scattering for quadratic-type Schrödinger systems in dimension five without mass-resonance pp. 1-30

Norman Noguera and Ademir Pastor

The Navier–Stokes equations on the plane with time-dependent external forces pp. 1-42

Masao Yamazaki

Describing limits of integrable functions as grid functions of nonstandard analysis pp. 1-25

Emanuele Bottazzi

Scattering resonances for a three-dimensional subwavelength hole pp. 1-25

Maryam Fatima and Junshan Lin

Regularity properties of the cubic biharmonic Schrödinger equation on the half line pp. 1-37

Engin Başakoğlu

Minimal brake orbits of first-order convex Hamiltonian systems with anisotropic growth pp. 1-8

Xiaofei Zhang and Chungen Liu

Volume 2, issue 3, 2021

On the uniqueness of a suitable weak solution to the Navier–Stokes Cauchy problem pp. 1-36

Francesca Crispo and Paolo Maremonti

Improved regularity criterion for the 3D Navier–Stokes equations via the gradient of one velocity component pp. 1-5

Sadek Gala and Maria Alessandra Ragusa

Convergence analysis of a Galerkin boundary element method for electromagnetic resonance problems pp. 1-29

Gerhard Unger

Attraction–repulsion taxis mechanisms in a predator–prey model pp. 1-29

Jonathan Bell and Evan C. Haskell

Regularity estimates for nonlocal equations with an asymptotic property pp. 1-13

Disson Prazeres and Aelson Sobral

On sublinear fractional Schrödinger–Poisson systems pp. 1-13

Abderrazek Benhassine

Remarks on the generalized Cauchy-Dirichlet problem for graph mean curvature flow with driving force pp. 1-24

Hiroyoshi Mitake and Longjie Zhang

On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations pp. 1-20

Fábio Natali, Eleomar Cardoso and Sabrina Amaral

The Keller–Segel system on bounded convex domains in critical spaces pp. 1-14

Matthias Hieber, Klaus Kress and Christian Stinner

Publisher Correction to: Diffusive limit of a two-dimensional well-balanced approximation to a kinetic model of chemotaxis pp. 1-1

Gabriella Bretti and Laurent Gosse

Multi-domain spectral approach for the Hilbert transform on the real line pp. 1-19

Christian Klein, Julien Riton and Nikola Stoilov

Volume 2, issue 2, 2021

Regularity of the m-symphonic map pp. 1-20

Masashi Misawa and Nobumitsu Nakauchi

On well-posedness of the Cauchy problem for 3D MHD system in critical Sobolev–Gevrey space pp. 1-20

Abdelkerim Chaabani

Analytical preconditioners for Neumann elastodynamic boundary element methods pp. 1-26

Stéphanie Chaillat, Marion Darbas and Frédérique Le Louër

On averaged exponential integrators for semilinear wave equations with solutions of low-regularity pp. 1-27

Simone Buchholz, Benjamin Dörich and Marlis Hochbruck

A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications pp. 1-27

Nao Hamamuki and Qing Liu

On the existence of positive solutions to a certain class of semilinear elliptic equations pp. 1-27

Norihisa Ikoma

An alternative proof of $$L^q$$ L q – $$L^r$$ L r estimates of the Oseen semigroup in higher dimensional exterior domains pp. 1-12

Toshiaki Hishida

On the Hölder regularity for solutions of integro-differential equations like the anisotropic fractional Laplacian pp. 1-34

E. B. dos Santos and R. Leitão

Diffusive limit of a two-dimensional well-balanced approximation to a kinetic model of chemotaxis pp. 1-34

Gabriella Bretti and Laurent Gosse

Uniform estimates for fractional operators pp. 1-18

Reinhard Farwig and Kazuyuki Tsuda

Some results on positive solutions of a Kirchhoff type problem with indefinite conditions pp. 1-22

Jiaqing Hu and Qiangqiang Yang

Fourth-order nonlocal type elliptic problems with indefinite nonlinearities pp. 1-22

Edcarlos D. Silva, J. C. Albuquerque and T. R. Cavalcante

Continuity of selected pullback attractors pp. 1-16

Rodrigo A. Samprogna and Jacson Simsen

A uniqueness result for the Sine-Gordon breather pp. 1-8

Rainer Mandel

Volume 2, issue 1, 2021

Existence and nonexistence results for critical growth fractional elliptic systems pp. 1-12

Fengshuang Gao and Yuxia Guo

Local existence and nonexistence for fractional in time weakly coupled reaction-diffusion systems pp. 1-27

Masamitsu Suzuki

Stochastic optimal transport revisited pp. 1-26

Toshio Mikami

Liouville type theorems for stationary Navier–Stokes equations pp. 1-20

Tai-Peng Tsai

Phase transitions arising in stochastic ergodic control associated with viscous Hamilton–Jacobi equations with bounded inward drift pp. 1-28

Naoyuki Ichihara

Concentration, existence of a ground state and multiplicity of solutions for a subcritical elliptic system via penalization method pp. 1-30

Giovany M. Figueiredo and Segundo Manuel A. Salirrosas

Existence, symmetries, and asymptotic properties of global solutions for a fractional diffusion equation with gradient nonlinearity pp. 1-30

Halley Gomes and Arlúcio Viana

Publisher Correction to: Dynamic boundary conditions and the Carslaw-Jaeger constitutive relation in heat transfer pp. 1-1

Niko Sauer

Publisher Correction to: Runge–Kutta approximation for C0-semigroups in the graph norm with applications to time domain boundary integral equations pp. 1-1

Alexander Rieder, Francisco-Javier Sayas and Jens Markus Melenk

Global existence of classical solutions to a chemotaxis-haptotaxis model pp. 1-15

Jozil Takhirov

Stationary mean-field games with logistic effects pp. 1-34

Diogo Aguiar Gomes and Ricardo de Lima Ribeiro

Existence of solution for a class of elliptic problems in exterior domain with discontinuous nonlinearity pp. 1-32

Claudianor O. Alves and Tuhina Mukherjee

Existence of ground state solutions of the coupled nonlinear Hartree type system with attractive couplings pp. 1-16

Jun Wang and Song Wei

Multilane analysis of a viscous second-order macroscopic traffic flow model pp. 1-17

Gabriel Obed Fosu, Francis Tabi Oduro and Carlo Caligaris

Phaseless inverse uniqueness of a three-dimensional scattering problem of second type pp. 1-10

Lung-Hui Chen

Precise blowup rate near the boundary of boundary blowup solutions to k-Hessian equation pp. 1-10

Kazuhiro Takimoto

Neural networks-based backward scheme for fully nonlinear PDEs pp. 1-24

Huyên Pham, Xavier Warin and Maximilien Germain