Partial Differential Equations and Applications

2020 - 2025

Current editor(s): Zhitao Zhang

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Volume 1, issue 6, 2020

Existence of multiple solutions to semilinear Dirichlet problem for subelliptic operator pp. 1-16

Hua Chen, Hong-Ge Chen and Xin-Rui Yuan

Runge–Kutta approximation for $$C_0$$ C 0 -semigroups in the graph norm with applications to time domain boundary integral equations pp. 1-47

Alexander Rieder, Francisco-Javier Sayas and Jens Markus Melenk

Viscosity solutions for the crystalline mean curvature flow with a nonuniform driving force term pp. 1-26

Yoshikazu Giga and Norbert Požár

Global existence of solutions to some equations modeling phase separation of self-propelled particles pp. 1-26

Hantaek Bae

Fourth-order time-stepping compact finite difference method for multi-dimensional space-fractional coupled nonlinear Schrödinger equations pp. 1-29

Mustafa Almushaira and Fei Liu

Asymptotic modelling of Skin-effects in coaxial cables pp. 1-34

Geoffrey Beck, Sébastien Imperiale and Patrick Joly

Finer analysis of the Nehari set associated to a class of Kirchhoff-type equations pp. 1-23

Kaye Silva and Steffânio M. Sousa

A logarithmically improved regularity criterion for the Boussinesq equations in a bounded domain pp. 1-11

Ahmad M. Alghamdi, Sadek Gala and Maria Alessandra Ragusa

Time harmonic wave propagation in one dimensional weakly randomly perturbed periodic media pp. 1-36

Sonia Fliss and Laure Giovangigli

All the generalized characteristics for the solution to a Hamilton–Jacobi equation with the initial data of the Takagi function pp. 1-20

Yasuhiro Fujita, Nao Hamamuki and Norikazu Yamaguchi

Helmholtz’s decomposition for compressible flows and its application to computational aeroacoustics pp. 1-20

Stefan Schoder, Klaus Roppert and Manfred Kaltenbacher

Dynamic boundary conditions and the Carslaw-Jaeger constitutive relation in heat transfer pp. 1-20

Niko Sauer

Volume 1, issue 5, 2020

Professor Dajun Guo: a true mathematician and educator pp. 1-10

Jinxian Sun, Xing-Bin Pan, Yihong Du, Zhaoli Liu and Zhitao Zhang

The Brezis–Nirenberg type double critical problem for the Choquard equation pp. 1-20

Li Cai and Fubao Zhang

Nodal bubble tower solutions to slightly subcritical elliptic problems with Hardy terms pp. 1-21

Thomas Bartsch and Qianqiao Guo

Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy pp. 1-18

Lishan Liu, Fenglong Sun and Yonghong Wu

On spectral asymptotics and bifurcation for Carrier equations with odd superlinear term pp. 1-14

Yu Zhang and Baoqiang Yan

Positive and negative solutions for the nonlinear fractional Kirchhoff equation in $${\mathbb {R}}^{N}$$ R N pp. 1-19

Yang Wang and Yansheng Liu

Nontrivial solutions to non-local problems with sublinear or superlinear nonlinearities pp. 1-19

Zhiqing Han and Ye Xue

Maxwell–Stokes system with $$L^2$$ L 2 boundary data and Div–Curl system with potential pp. 1-56

Xing-Bin Pan

Sign-changing and constant-sign solutions for elliptic problems involving nonlocal integro-differential operators pp. 1-17

Huiqin Lu, Xinmin Qu and Jianing Wang

Partial symmetry of normalized solutions for a doubly coupled Schrödinger system pp. 1-15

Haijun Luo and Zhitao Zhang

Strictly convex solutions for singular Monge–Ampère equations with nonlinear gradient terms: existence and boundary asymptotic behavior pp. 1-15

Meiqiang Feng, Huayuan Sun and Xuemei Zhang

Minimal submanifolds in a metric measure space pp. 1-15

Xu Cheng and Detang Zhou

Propagation, diffusion and free boundaries pp. 1-25

Yihong Du

Normalized solutions for a class of nonlinear Choquard equations pp. 1-25

Thomas Bartsch, Yanyan Liu and Zhaoli Liu

Volume 1, issue 4, 2020

Stability analysis of a delayed sir epidemic model with diffusion and saturated incidence rate pp. 1-25

Abdelhadi Abta, Salahaddine Boutayeb, Hassan Laarabi, Mostafa Rachik and Hamad Talibi Alaoui

A discontinuous Galerkin Trefftz type method for solving the two dimensional Maxwell equations pp. 1-25

Håkon Sem Fure, Sébastien Pernet, Margot Sirdey and Sébastien Tordeux

Partial regularity of weak solutions and life-span of smooth solutions to a biological network formulation model pp. 1-31

Xiangsheng Xu

Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form pp. 1-16

Xiaoqin Guo, Hung V. Tran and Yifeng Yu

Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation pp. 1-26

A. Gibbs, D. P. Hewett, D. Huybrechs and E. Parolin

Sweeping preconditioners for stratified media in the presence of reflections pp. 1-17

Janosch Preuß, Thorsten Hohage and Christoph Lehrenfeld

Structure aware Runge–Kutta time stepping for spacetime tents pp. 1-24

Jay Gopalakrishnan, Joachim Schöberl and Christoph Wintersteiger

ABP maximum principles for fully nonlinear integro-differential equations with unbounded inhomogeneous terms pp. 1-11

Shuhei Kitano

Formulation of a maximum principle satisfying a numerical scheme for traffic flow models pp. 1-11

Oluwaseun Farotimi and Kuppalapalle Vajravelu

A game theoretical approach for a nonlinear system driven by elliptic operators pp. 1-41

Alfredo Miranda and Julio D. Rossi

Existence of solutions for a class of IBVP for nonlinear hyperbolic equations pp. 1-20

Svetlin Georgiev Georgiev and Mohamed Majdoub

Volume 1, issue 3, 2020

Asymptotic behavior for a class of derivative nonlinear Schrödinger systems pp. 1-41

Soichiro Katayama and Daisuke Sakoda

The topological contribution of the critical points at infinity for critical fractional Yamabe-type equations pp. 1-26

Khadijah Abdullah Sharaf and Hichem Chtioui

Volume 1, issue 2, 2020

Existence of positive solutions to Kirchhoff equations with vanishing potentials and general nonlinearity pp. 1-12

Dongdong Sun and Zhitao Zhang

Entropy stable h/p-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier–Stokes equations pp. 1-54

David C. Del Rey Fernández, Mark H. Carpenter, Lisandro Dalcin, Stefano Zampini and Matteo Parsani

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations pp. 1-34

Martin Hutzenthaler, Arnulf Jentzen, Thomas Kruse and Tuan Anh Nguyen

Numerical continuation for a fast-reaction system and its cross-diffusion limit pp. 1-26

Christian Kuehn and Cinzia Soresina

Volume 1, issue 1, 2020

Decay in the one dimensional generalized Improved Boussinesq equation pp. 1-20

Christopher Maulén and Claudio Muñoz

Long time behavior of a model for the evolution of morphogens in a growing tissue pp. 1-39

G. M. Coclite and M. M. Coclite

The exterior Calderón operator for non-spherical objects pp. 1-32

Gerhard Kristensson, Ioannis G. Stratis, Niklas Wellander and Athanasios N. Yannacopoulos

Hardy type inequalities with spherical derivatives pp. 1-15

Neal Bez, Shuji Machihara and Tohru Ozawa

The effects of convolution and gradient dependence on a parametric Dirichlet problem pp. 1-15

Dumitru Motreanu, Calogero Vetro and Francesca Vetro

Characterization of harmonic functions by the behavior of means at a single point pp. 1-13

Ricardo Estrada