1. Theory of PDEs

Articles (105 in this collection)

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

   Authors

   • E. Compaan
   • N. Tzirakis

   • Content type: Original Paper
   • Published: 26 October 2023

   • Article: 48

2. Besov regularity of inhomogeneous parabolic PDEs

   Authors

   • Cornelia Schneider
   • Flóra Orsolya Szemenyei

   • Content type: Original Paper
   • Open Access
   • Published: 16 September 2023

   • Article: 43

   

3. Semiclassical states of a type of Dirac–Klein–Gordon equations with nonlinear interacting terms

   Authors

   • Yanheng Ding
   • Qi Guo
   • Yuanyang Yu

   • Content type: Original Paper
   • Published: 09 September 2023

   • Article: 42

   

4. On the range of unsolvable systems induced by complex vector fields

   Authors

   • A. V. da Silva Jr

   • Content type: Original Paper
   • Open Access
   • Published: 01 September 2023

   • Article: 41

   

5. Energy equality of MHD system under a weaker condition on magnetic field

   Authors

   • Taichi Eguchi

   • Content type: Original Paper
   • Open Access
   • Published: 08 August 2023

   • Article: 39

6. On the motion of the director field of a nematic liquid crystal submitted to a magnetic field and a laser beam

   Authors

   • Paulo Amorim
   • João-Paulo Dias
   • Assis F. Martins

   • Content type: Original Paper
   • Published: 21 July 2023

   • Article: 36

   

7. A regularized system for the nonlinear variational wave equation

   Authors

   • Katrin Grunert
   • Audun Reigstad

   • Content type: Original Paper
   • Open Access
   • Published: 20 July 2023

   • Article: 35

   

8. Choquard equations with mixed potential

   Authors

   • Romildo N. de Lima
   • Marco A. S. Souto

   • Content type: Original Paper
   • Published: 13 July 2023

   • Article: 33

9. Nonlinear semigroups for nonlocal conservation laws

   Authors

   • Mihály Kovács
   • Mihály A. Vághy

   • Content type: Original Paper
   • Open Access
   • Published: 08 July 2023

   • Article: 32

10. Fourth-order nonlinear degenerate problem for image decomposition

    Authors

    • Ahmed Nokrane
    • Nour Eddine Alaa
    • Fatima Aqel

    • Content type: Original Paper
    • Published: 07 July 2023

    • Article: 31

    

11. On an indefinite nonhomogeneous equation with critical exponential growth

    Authors

    • Karla Carolina V. de Sousa
    • Leandro S. Tavares

    • Content type: Original Paper
    • Published: 14 June 2023

    • Article: 28

    

12. Asymptotics of solutions for the fractional modified Korteweg–de Vries equation of order \(\alpha \in \left( 2,3\right) \)

    Authors

    • Rafael Carreño-Bolaños
    • Nakao Hayashi
    • Pavel I. Naumkin

    • Content type: Original Paper
    • Published: 05 June 2023

    • Article: 26

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

    Authors

    • Keisuke Abiko

    • Content type: Original Paper
    • Published: 02 June 2023

    • Article: 24

14. Global logarithmic stability of a Cauchy problem for anisotropic wave equations

    Authors

    • Mourad Bellassoued
    • Mourad Choulli

    • Content type: Original Paper
    • Published: 30 May 2023

    • Article: 23

15. Uniform stability of a thermodiffusion Timoshenko beam

    Authors

    • Fayssal Djellali
    • Tijani A. Apalara
    • Mohamed Zitouni

    • Content type: Original Paper
    • Published: 30 May 2023

    • Article: 22

16. On the antimaximum principle for the p-Laplacian and its sublinear perturbations

    Authors

    • Vladimir Bobkov
    • Mieko Tanaka

    • Content type: Original Research Article
    • Published: 25 May 2023

    • Article: 21

    

17. General decay of the solution to a nonlinear viscoelastic beam with delay

    Authors

    • Ammar Khemmoudj

    • Content type: Original Paper
    • Published: 08 May 2023

    • Article: 20

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

    Authors

    • Pascal Remy

    • Content type: Original Research Article
    • Published: 01 May 2023

    • Article: 19

    

19. Existence of solutions for resonant double phase problems with mixed boundary value conditions

    Authors (first, second and last of 4)

    • Yihao Yang
    • Wulong Liu
    • Xingye Yan

    • Content type: Original Research Article
    • Open Access
    • Published: 26 April 2023

    • Article: 18

20. A remake of Bourgain–Brezis–Mironescu characterization of Sobolev spaces

    Authors

    • Guy Fabrice Foghem Gounoue

    • Content type: Original Paper
    • Open Access
    • Published: 24 March 2023

    • Article: 16

21. Observability for Schrödinger equations with quadratic Hamiltonians

    Authors

    • Alden Waters

    • Content type: Original Paper
    • Open Access
    • Published: 08 March 2023

    • Article: 12

    

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

    Authors

    • Émile Deléage
    • Felipe Linares

    • Content type: Original Paper
    • Published: 24 February 2023

    • Article: 9

23. Local bounds of the gradient of weak solutions to the porous medium equation

    Authors

    • Ugo Gianazza
    • Juhana Siljander

    • Content type: Original Paper
    • Published: 22 February 2023

    • Article: 8

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

    Authors

    • Claudianor O. Alves
    • Tahir Boudjeriou

    • Content type: Original Paper
    • Published: 14 February 2023

    • Article: 5

    

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

    Authors

    • Giuseppe Maria Coclite
    • Lorenzo di Ruvo

    • Content type: Original Paper
    • Open Access
    • Published: 16 November 2022

    • Article: 79

26. Large time asymptotics for the fractional modified Korteweg-de Vries equation with \(\alpha \in \left( 2,4\right) \)

    Authors

    • Nakao Hayashi
    • Pavel I. Naumkin
    • Isahi Sánchez-Suárez

    • Content type: Original Paper
    • Published: 21 October 2022

    • Article: 76

27. Higher integrability for doubly nonlinear parabolic systems

    Authors

    • Verena Bögelein
    • Frank Duzaar
    • Christoph Scheven

    • Content type: Original Paper
    • Open Access
    • Published: 18 October 2022

    • Article: 74

    

28. Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the \(L^p\) framework

    Authors

    • Hua Qiu
    • Zheng-an Yao

    • Content type: Original Paper
    • Published: 18 October 2022

    • Article: 73

29. Stability of mKdV breathers on the half-line

    Authors

    • Miguel A. Alejo
    • Márcio Cavalcante
    • Adán J. Corcho

    • Content type: Original Paper
    • Published: 10 October 2022

    • Article: 70

    

30. Energy asymptotics for the strongly damped Klein–Gordon equation

    Authors

    • Haidar Mohamad

    • Content type: Original Paper
    • Open Access
    • Published: 10 October 2022

    • Article: 71

    

31. Normalized solutions of Kirchhoff equations with critical and subcritical nonlinearities: the defocusing case

    Authors

    • Paulo C. Carrião
    • Olímpio H. Miyagaki
    • André Vicente

    • Content type: Original Paper
    • Published: 19 September 2022

    • Article: 64

32. Large-time behaviour of solutions to the surface quasi-geostrophic equation

    Authors

    • Dáithí Ó hAodha
    • Tsukasa Iwabuchi

    • Content type: Original Paper
    • Published: 06 September 2022

    • Article: 60

33. Nonlinear schrödinger equations with the third order dispersion on modulation spaces

    Authors

    • X. Carvajal
    • M. Panthee

    • Content type: Original Paper
    • Published: 06 September 2022

    • Article: 59

34. Orbital stability and instability of periodic wave solutions for the \(\phi ^4\)-model

    Authors

    • José Manuel Palacios

    • Content type: Original Paper
    • Published: 08 August 2022

    • Article: 56

    

35. A Duistermaat–Heckman type formula for the based loop group

    Authors

    • Jack Ding
    • Lisa Jeffrey

    • Content type: Original Paper
    • Published: 03 August 2022

    • Article: 55

36. Weak–strong uniqueness for the isentropic Euler equations with possible vacuum

    Authors

    • Shyam Sundar Ghoshal
    • Animesh Jana
    • Emil Wiedemann

    • Content type: Original Paper
    • Published: 29 July 2022

    • Article: 54

37. Rectifiability of divergence-free fields along invariant 2-tori

    Authors

    • David Perrella
    • David Pfefferlé
    • Luchezar Stoyanov

    • Content type: Original Paper
    • Open Access
    • Published: 11 July 2022

    • Article: 50

38. Threshold odd solutions to the nonlinear Schrödinger equation in one dimension

    Authors

    • Stephen Gustafson
    • Takahisa Inui

    • Content type: Original Paper
    • Published: 01 July 2022

    • Article: 46

39. The Gauss map of minimal surfaces in \({\mathbb {S}}^2 \times {\mathbb {R}}\)

    Authors

    • Iury Domingos

    • Content type: Original Paper
    • Published: 16 May 2022

    • Article: 40

    

40. Transport equations with inflow boundary conditions

    Authors

    • L. Ridgway Scott
    • Sara Pollock

    • Content type: Original Research Article
    • Published: 30 April 2022

    • Article: 35

    

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

    Authors

    • Hartmut Pecher

    • Content type: Original Paper
    • Open Access
    • Published: 10 April 2022

    • Article: 33

42. Applications of p-harmonic transplantation for functional inequalities involving a Finsler norm

    Authors

    • Sadaf Habibi
    • Futoshi Takahashi

    • Content type: Original Research Article
    • Published: 07 April 2022

    • Article: 32

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

    Authors

    • Jianjun Zhang
    • Diego Felix
    • Everaldo Medeiros

    • Content type: Original Paper
    • Published: 05 April 2022

    • Article: 30

    

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

    Authors

    • Yuki Osada

    • Content type: Original Paper
    • Published: 23 March 2022

    • Article: 28

45. Calderón-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient

    Authors (first, second and last of 4)

    • Mouhamed Moustapha Fall
    • Tadele Mengesha
    • Sasikarn Yeepo

    • Content type: Original Paper
    • Published: 21 March 2022

    • Article: 24

46. Ground states for Maxwell’s equations in nonlocal nonlinear media

    Authors

    • Rainer Mandel

    • Content type: Original Paper
    • Open Access
    • Published: 09 March 2022

    • Article: 22

47. Existence and decay of global solutions for the Kuramoto–Sivashinsky–Zakharov–Kuznetsov equation posed on rectangles

    Authors

    • N. A. Larkin

    • Content type: Original Paper
    • Published: 22 February 2022

    • Article: 20

48. Ground state solution for nonlocal scalar field equations involving an integro-differential operator

    Authors

    • Ronaldo C. Duarte

    • Content type: Original Paper
    • Published: 18 February 2022

    • Article: 19

    

49. Strichartz estimates for quadratic repulsive potentials

    Authors

    • Masaki Kawamoto
    • Taisuke Yoneyama

    • Content type: Original Paper
    • Published: 28 January 2022

    • Article: 15

    

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

    Authors

    • Gaku Hoshino

    • Content type: Original Paper
    • Published: 26 January 2022

    • Article: 14