Partial Differential Equations and Applications

2020 - 2025

Current editor(s): Zhitao Zhang

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Volume 3, issue 6, 2022

On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation pp. 1-40

Giuseppe Maria Coclite and Lorenzo Ruvo

Energy asymptotics for the strongly damped Klein–Gordon equation pp. 1-12

Haidar Mohamad

Higher integrability for doubly nonlinear parabolic systems pp. 1-41

Verena Bögelein, Frank Duzaar and Christoph Scheven

Similarity solutions for imploding strong shock waves in a van der Waals gas pp. 1-22

Ankita Sharma and Rajan Arora

Families of solutions to the KPI equation given by an extended Darboux transformation pp. 1-14

Pierre Gaillard

Large time asymptotics for the fractional modified Korteweg-de Vries equation with $$\alpha \in \left( 2,4\right) $$ α ∈ 2, 4 pp. 1-28

Nakao Hayashi, Pavel I. Naumkin and Isahi Sánchez-Suárez

Exhaustive existence and non-existence results for Hardy–Hénon equations in $${{\,\mathrm{{\textbf{R}}}\,}}^n$$ R n pp. 1-38

Yoshikazu Giga and Quốc Anh Ngô

Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the $$L^p$$ L p framework pp. 1-38

Hua Qiu and Zheng-an Yao

Finite element approximation of invariant manifolds by the parameterization method pp. 1-38

Jorge Gonzalez, J. D. Mireles James and Necibe Tuncer

Stability of mKdV breathers on the half-line pp. 1-21

Miguel A. Alejo, Márcio Cavalcante and Adán J. Corcho

From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications pp. 1-26

J. Franceschi, L. Pareschi and M. Zanella

Existence and non-existence of global solutions for a heat equation with degenerate coefficients pp. 1-16

Ricardo Castillo, Omar Guzmán-Rea and María Zegarra

Deep learning schemes for parabolic nonlocal integro-differential equations pp. 1-35

Javier Castro

Nonlinear fractional Schrödinger equation on the half-Line pp. 1-27

Gerardo Huaroto

A time-periodic reaction-diffusion population model of a species subjected to harvesting on the boundary of a protected habitat pp. 1-19

K. D. Searle and J. H. Vuuren

Volume 3, issue 5, 2022

On a hybrid continuum-kinetic model for complex fluids pp. 1-28

A. Chertock, P. Degond, G. Dimarco, M. Lukáčová-Medvid’ová and A. Ruhi

Uniform convergent scheme for discrete-ordinate radiative transport equation with discontinuous coefficients on unstructured quadrilateral meshes pp. 1-20

Yihong Wang, Min Tang and Jingyi Fu

Nonlinear schrödinger equations with the third order dispersion on modulation spaces pp. 1-21

X. Carvajal and M. Panthee

Functional analytic properties and regularity of the Möbius-invariant Willmore flow in $${\mathbf {R}}^n$$ R n pp. 1-48

Ruben Jakob

The effect of the domain topology on the number of positive solutions for an elliptic system pp. 1-23

Giovany M. Figueiredo and Leticia S. Silva

Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains pp. 1-32

Giancarlo Consolo and Gabriele Grifó

Large-time behaviour of solutions to the surface quasi-geostrophic equation pp. 1-17

Dáithí Ó hAodha and Tsukasa Iwabuchi

Secondary bifurcations in semilinear ordinary differential equations pp. 1-39

Toru Kan

Sobolev spaces and functions of Marcinkiewicz type with repeated averaging operations over spheres pp. 1-19

Shuichi Sato

Editorial pp. 1-2

Manfred Kaltenbacher and Jens Markus Melenk

Normalized solutions of Kirchhoff equations with critical and subcritical nonlinearities: the defocusing case pp. 1-16

Paulo C. Carrião, Olímpio H. Miyagaki and André Vicente

Volume 3, issue 4, 2022

Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms pp. 1-41

Philipp Grohs, Arnulf Jentzen and Diyora Salimova

Rectifiability of divergence-free fields along invariant 2-tori pp. 1-32

David Perrella, David Pfefferlé and Luchezar Stoyanov

Orbital stability and instability of periodic wave solutions for the $$\phi ^4$$ ϕ 4 -model pp. 1-31

José Manuel Palacios

Preface pp. 1-9

Kazuhiro Ishige, Tohru Ozawa, Senjo Shimizu and Yasushi Taniuchi

Numerical methods for the hyperbolic Monge-Ampère equation based on the method of characteristics pp. 1-42

M. W. M. C. Bertens, E. M. T. Vugts, M. J. H. Anthonissen, J. H. M. Thije Boonkkamp and W. L. IJzerman

Weak–strong uniqueness for the isentropic Euler equations with possible vacuum pp. 1-21

Shyam Sundar Ghoshal, Animesh Jana and Emil Wiedemann

Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties pp. 1-30

Andrea Medaglia, Andrea Tosin and Mattia Zanella

Asymptotic analysis of subwavelength halide perovskite resonators pp. 1-28

Konstantinos Alexopoulos and Bryn Davies

Threshold odd solutions to the nonlinear Schrödinger equation in one dimension pp. 1-45

Stephen Gustafson and Takahisa Inui

A Duistermaat–Heckman type formula for the based loop group pp. 1-16

Jack Ding and Lisa Jeffrey

Large-time behavior of solutions of parabolic equations on the real line with convergent initial data III: unstable limit at infinity pp. 1-27

Antoine Pauthier and Peter Poláčik

Oscillatory decay in a degenerate parabolic equation pp. 1-15

Michael Winkler

Discontinuous stationary solutions to certain reaction-diffusion systems pp. 1-15

Szymon Cygan, Anna Marciniak-Czochra and Grzegorz Karch

Volume 3, issue 3, 2022

A method of fundamental solutions with time-discretisation for wave motion from lateral Cauchy data pp. 1-13

Ihor Borachok, Roman Chapko and B. Tomas Johansson

Dirichlet spectral-Galerkin approximation method for the simply supported vibrating plate eigenvalues pp. 1-16

Isaac Harris

Global existence of solutions of area-preserving curvature flow of a convex plane curve in an inhomogeneous medium pp. 1-16

R. Lui and H. Ninomiya

Local well-posedness of the coupled Yang–Mills and Dirac system in temporal gauge pp. 1-23

Hartmut Pecher

Applications of p-harmonic transplantation for functional inequalities involving a Finsler norm pp. 1-17

Sadaf Habibi and Futoshi Takahashi

Second-order diffusion limit for the phonon transport equation: asymptotics and numerics pp. 1-17

Anjali Nair, Qin Li and Weiran Sun

Heat equation with an exponential nonlinear boundary condition in the half space pp. 1-44

Giulia Furioli, Tatsuki Kawakami and Elide Terraneo

Transport equations with inflow boundary conditions pp. 1-20

L. Ridgway Scott and Sara Pollock

The Gauss map of minimal surfaces in $${\mathbb {S}}^2 \times {\mathbb {R}}$$ S 2 × R pp. 1-20

Iury Domingos

A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon pp. 1-20

Andrew Haar and Petronela Radu

Relativistic Kinetic Theory of Polyatomic Gases: Classical Limit of a New Hierarchy of Moments and Qualitative Analysis pp. 1-21

Takashi Arima, Maria Cristina Carrisi, Sebastiano Pennisi and Tommaso Ruggeri

Cauchy problem for the ES-BGK model with the correct Prandtl number pp. 1-9

Sung-jun Son and Seok-Bae Yun

Volume 3, issue 2, 2022

Ground state solution for nonlocal scalar field equations involving an integro-differential operator pp. 1-14

Ronaldo C. Duarte

Time-periodic flows of magnetic fluids pp. 1-24

Jáuber C. Oliveira

Global in time solvability for a semilinear heat equation without the self-similar structure pp. 1-32

Yohei Fujishima and Norisuke Ioku

Existence of a minimizer for a nonlinear Schrödinger system with three wave interaction under non-symmetric potentials pp. 1-18

Yuki Osada

Dynamical universality for random matrices pp. 1-51

Yosuke Kawamoto and Hirofumi Osada

Preface pp. 1-2

Shigeaki Koike

On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model pp. 1-16

Geni Gupur

Ground states for Maxwell’s equations in nonlocal nonlinear media pp. 1-16

Rainer Mandel

Liouville theorems for parabolic systems with homogeneous nonlinearities and gradient structure pp. 1-16

Pavol Quittner

Entire solutions with moving singularities for a semilinear heat equation with a critical exponent pp. 1-16

Jin Takahashi

Existence and decay of global solutions for the Kuramoto–Sivashinsky–Zakharov–Kuznetsov equation posed on rectangles pp. 1-17

N. A. Larkin

On a sharp weighted Sobolev inequality on the upper half-space and its applications pp. 1-17

Jianjun Zhang, Diego Felix and Everaldo Medeiros

Rotational self-friction problem of elastic rods pp. 1-17

Mohamed Ali Latrach and Mourad Chamekh

Existence and multiplicity of solutions for Schrödinger equations with asymptotically linear nonlinearities allowing interaction with essential spectrum pp. 1-19

Linjie Song

Calderón-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient pp. 1-27

Mouhamed Moustapha Fall, Tadele Mengesha, Armin Schikorra and Sasikarn Yeepo

Volume 3, issue 1, 2022

On refined blowup estimates for the exponential reaction-diffusion equation pp. 1-9

Philippe Souplet

Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime pp. 1-10

Kimitoshi Tsutaya and Yuta Wakasugi

Space-time analytic smoothing effect for the cubic nonlinear Schrödinger equations without pseudo-conformal invariance pp. 1-21

Gaku Hoshino

(Non-)convergence of solutions of the convective Allen–Cahn equation pp. 1-11

Helmut Abels

Continuum of positive solutions of superlinear fractional Laplacian problems pp. 1-11

Maya Chhetri, Petr Girg and Elliott Hollifield

McKean–Vlasov type stochastic differential equations arising from the random vortex method pp. 1-22

Zhongmin Qian and Yuhan Yao

Existence and nonexistence of solutions to nonlocal elliptic problems pp. 1-32

Hamilton Bueno, Gilberto A. Pereira, Edcarlos D. Silva and Ricardo Ruviaro

Strichartz estimates for quadratic repulsive potentials pp. 1-12

Masaki Kawamoto and Taisuke Yoneyama

Newton’s second law with a semiconvex potential pp. 1-34

Ryan Hynd

Local regularity conditions on initial data for local energy solutions of the Navier–Stokes equations pp. 1-19

Kyungkeun Kang, Hideyuki Miura and Tai-Peng Tsai

Equivalences of PDE systems associated to degenerate para-CR structures: foundational aspects pp. 1-57

Joël Merker

Local minimality properties of circular motions in $$1/r^\alpha $$ 1 / r α potentials and of the figure-eight solution of the 3-body problem pp. 1-17

M. Fenucci

A posteriori verification of the positivity of solutions to elliptic boundary value problems pp. 1-25

Kazuaki Tanaka and Taisei Asai

Sobolev estimates for non-uniformly parabolic PDEs pp. 1-25

Steve Schochet

On some regularity results of parabolic problems with nonlinear perturbed terms and general data pp. 1-39

M. Abdellaoui and H. Redwane

Maximal regularity and a singular limit problem for the Patlak–Keller–Segel system in the scaling critical space involving BMO pp. 1-56

Masaki Kurokiba and Takayoshi Ogawa