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Communications on Pure & Applied Analysis (ISSN 1534-0392) is published monthly. CPAA is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included. It features recent development in analysis and its applications, with a central theme on theoretical and numeric differential equations and applications. It is edited by some leading researchers to guarantee the journal's highest standard and closest link to the scientific communities.

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A second-order accurate structure-preserving scheme for the Cahn-Hilliard equation with a dynamic boundary condition
Makoto Okumura, Takeshi Fukao, Daisuke Furihata and Shuji Yoshikawa
2022, 21(2) : 355-392 doi: 10.3934/cpaa.2021181 +[Abstract](287) +[HTML](121) +[PDF](1379.59KB)
A convergent finite difference method for computing minimal Lagrangian graphs
Brittany Froese Hamfeldt and Jacob Lesniewski
2022, 21(2) : 393-418 doi: 10.3934/cpaa.2021182 +[Abstract](205) +[HTML](85) +[PDF](2120.16KB)
Variation and oscillation for harmonic operators in the inverse Gaussian setting
Víctor Almeida and Jorge J. Betancor
2022, 21(2) : 419-470 doi: 10.3934/cpaa.2021183 +[Abstract](178) +[HTML](86) +[PDF](361.97KB)
Global well-posedness in a chemotaxis system with oxygen consumption
Xujie Yang
2022, 21(2) : 471-492 doi: 10.3934/cpaa.2021184 +[Abstract](221) +[HTML](110) +[PDF](207.36KB)
Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum
Xin Zhong
2022, 21(2) : 493-515 doi: 10.3934/cpaa.2021185 +[Abstract](256) +[HTML](118) +[PDF](202.38KB)
On a nonlinear Laplace equation related to the boundary Yamabe problem in the upper-half space
Gael Diebou Yomgne
2022, 21(2) : 517-539 doi: 10.3934/cpaa.2021186 +[Abstract](233) +[HTML](109) +[PDF](245.93KB)
Liouville type theorems for stable solutions of elliptic system involving the Grushin operator
Foued Mtiri
2022, 21(2) : 541-553 doi: 10.3934/cpaa.2021187 +[Abstract](225) +[HTML](108) +[PDF](155.22KB)
Wave breaking phenomena and global existence for the weakly dissipative generalized Camassa-Holm equation
Yonghui Zhou and Shuguan Ji
2022, 21(2) : 555-566 doi: 10.3934/cpaa.2021188 +[Abstract](252) +[HTML](113) +[PDF](147.67KB)
Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system in $ \mathbb{R}^3 $ nonlinear KGS system
Salah Missaoui
2022, 21(2) : 567-584 doi: 10.3934/cpaa.2021189 +[Abstract](178) +[HTML](86) +[PDF](174.87KB)
On a system of nonlinear pseudoparabolic equations with Robin-Dirichlet boundary conditions
Le Thi Phuong Ngoc, Khong Thi Thao Uyen, Nguyen Huu Nhan and Nguyen Thanh Long
2022, 21(2) : 585-623 doi: 10.3934/cpaa.2021190 +[Abstract](222) +[HTML](74) +[PDF](292.65KB)
Blowing-up solutions for a supercritical elliptic equation
Yessine Dammak
2022, 21(2) : 625-637 doi: 10.3934/cpaa.2021191 +[Abstract](215) +[HTML](79) +[PDF](171.44KB)
Synchronized and ground-state solutions to a coupled Schrödinger system
Mohammad Ali Husaini and Chuangye Liu
2022, 21(2) : 639-667 doi: 10.3934/cpaa.2021192 +[Abstract](255) +[HTML](104) +[PDF](248.39KB)
Multiple non-radially symmetrical nodal solutions for the Schrödinger system with positive quasilinear term
Jianqing Chen and Qian Zhang
2022, 21(2) : 669-686 doi: 10.3934/cpaa.2021193 +[Abstract](182) +[HTML](91) +[PDF](194.38KB)
Nonnegative solutions to a doubly degenerate nutrient taxis system
Genglin Li and Michael Winkler
2022, 21(2) : 687-704 doi: 10.3934/cpaa.2021194 +[Abstract](177) +[HTML](78) +[PDF](199.34KB)
Bifurcation, uniqueness and multiplicity results for classes of reaction diffusion equations arising in ecology with nonlinear boundary conditions
Mohan Mallick, Sarath Sasi, R. Shivaji and S. Sundar
2022, 21(2) : 705-726 doi: 10.3934/cpaa.2021195 +[Abstract](251) +[HTML](61) +[PDF](317.11KB)
Necessary and sufficient conditions on weighted multilinear fractional integral inequality
Yongliang Zhou, Yangkendi Deng, Di Wu and Dunyan Yan
2022, 21(2) : 727-747 doi: 10.3934/cpaa.2021196 +[Abstract](141) +[HTML](54) +[PDF](177.35KB)
Uniqueness and sign properties of minimizers in a quasilinear indefinite problem
Uriel Kaufmann, Humberto Ramos Quoirin and Kenichiro Umezu
2021doi: 10.3934/10.3934/cpaa.2021078 +[Abstract](620) +[HTML](334) +[PDF](319.8KB)
On the attractor for a semilinear wave equation with variable coefficients and nonlinear boundary dissipation
Jiacheng Wang and Peng-Fei Yao
2021doi: 10.3934/cpaa.2021043 +[Abstract](767) +[HTML](372) +[PDF](317.63KB)
Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations
Juan Wen, Yaling He, Yinnian He and Kun Wang
2021doi: 10.3934/cpaa.2021074 +[Abstract](712) +[HTML](320) +[PDF](3024.82KB)
On the even solutions of the Toda system: a degree argument approach
Yong Liu, Jing Tian and Xuelin Yong
2021doi: 10.3934/cpaa.2021075 +[Abstract](582) +[HTML](320) +[PDF](782.03KB)
Hadamard Semidifferential, Oriented Distance Function, and some Applications
Michel C. Delfour
2021doi: 10.3934/cpaa.2021076 +[Abstract](729) +[HTML](322) +[PDF](482.37KB)
Analysis of COVID-19 epidemic transmission trend based on a time-delayed dynamic model
Tailei Zhang and Zhimin Li
2021doi: 10.3934/cpaa.2021088 +[Abstract](700) +[HTML](418) +[PDF](468.47KB)
Data-driven optimal control of a seir model for COVID-19
Hailiang Liu and Xuping Tian
2021doi: 10.3934/cpaa.2021093 +[Abstract](745) +[HTML](321) +[PDF](1372.32KB)
A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion
Jisheng Kou, Huangxin Chen, Xiuhua Wang and Shuyu Sun
2021doi: 10.3934/cpaa.2021094 +[Abstract](594) +[HTML](408) +[PDF](1366.37KB)
Ground state solutions for the fractional problems with dipole-type potential and critical exponent
Yu Su and Zhaosheng Feng
2021doi: 10.3934/cpaa.2021111 +[Abstract](495) +[HTML](269) +[PDF](326.3KB)
An indirect BIE free of degenerate scales
Jeng-Tzong Chen, Shing-Kai Kao, Jeng-Hong Kao and Wei-Chen Tai
2021doi: 10.3934/cpaa.2021114 +[Abstract](482) +[HTML](222) +[PDF](1662.62KB)
Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping
Zengji Du, Xiaojie Lin and Yulin Ren
2021doi: 10.3934/cpaa.2021118 +[Abstract](404) +[HTML](273) +[PDF](354.38KB)
Semi-discrete and fully discrete HDG methods for Burgers' equation
Zimo Zhu, Gang Chen and Xiaoping Xie
2021doi: 10.3934/cpaa.2021132 +[Abstract](491) +[HTML](264) +[PDF](488.08KB)
Spreading speed and periodic traveling waves of a time periodic and diffusive SI epidemic model with demographic structure
Shuang-Ming Wang, Zhaosheng Feng, Zhi-Cheng Wang and Liang Zhang
2021doi: 10.3934/cpaa.2021145 +[Abstract](487) +[HTML](251) +[PDF](502.96KB)
Dynamical analysis in disease transmission and final epidemic size
Daifeng Duan, Cuiping Wang and Yuan Yuan
2021doi: 10.3934/cpaa.2021150 +[Abstract](375) +[HTML](175) +[PDF](961.2KB)
Spatial dynamic analysis for COVID-19 epidemic model with diffusion and Beddington-DeAngelis type incidence
Tao Zheng, Yantao Luo, Xinran Zhou, Long Zhang and Zhidong Teng
2021doi: 10.3934/cpaa.2021154 +[Abstract](490) +[HTML](202) +[PDF](1057.49KB)
Transmission dynamics and high infectiousness of Coronavirus Disease 2019
Shunxiang Huang, Lin Wu, Jing Li, Ming-Zhen Xin, Yingying Wang, Xingjie Hao, Zhongyi Wang, Qihong Deng and Bin-Guo Wang
2021doi: 10.3934/cpaa.2021155 +[Abstract](384) +[HTML](182) +[PDF](1835.77KB)
Controllability and stabilization of gravity-capillary surface water waves in a basin
Jing Cui, Guangyue Gao and Shu-Ming Sun
2021doi: 10.3934/cpaa.2021158 +[Abstract](323) +[HTML](172) +[PDF](472.33KB)
Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru
Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh and Rana Parshad
2021doi: 10.3934/cpaa.2021170 +[Abstract](301) +[HTML](247) +[PDF](2334.82KB)
Time analyticity of the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations
Chulan Zeng
2021doi: 10.3934/cpaa.2021197 +[Abstract](137) +[HTML](77) +[PDF](273.85KB)
A flow method for a generalization of $ L_{p} $ Christofell-Minkowski problem
Boya Li, Hongjie Ju and Yannan Liu
2021doi: 10.3934/cpaa.2021198 +[Abstract](149) +[HTML](65) +[PDF](142.06KB)
Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities
Qi Wang and Yanyan Zhang
2021doi: 10.3934/cpaa.2021199 +[Abstract](156) +[HTML](60) +[PDF](218.45KB)
On regularity and stability for a class of nonlocal evolution equations with nonlinear perturbations
Dinh-Ke Tran and Nhu-Thang Nguyen
2021doi: 10.3934/cpaa.2021200 +[Abstract](252) +[HTML](64) +[PDF](169.47KB)
Radial symmetry of nonnegative solutions for nonlinear integral systems
Zhenjie Li and Chunqin Zhou
2021doi: 10.3934/cpaa.2021201 +[Abstract](154) +[HTML](56) +[PDF](118.6KB)
Analysis of Brinkman-Forchheimer extended Darcy's model in a fluid saturated anisotropic porous channel
Timir Karmakar, Meraj Alam and G. P. Raja Sekhar
2021doi: 10.3934/cpaa.2022001 +[Abstract](142) +[HTML](41) +[PDF](874.91KB)
Improved Hardy-Rellich inequalities
Biagio Cassano, Lucrezia Cossetti and Luca Fanelli
2021doi: 10.3934/cpaa.2022002 +[Abstract](102) +[HTML](57) +[PDF](227.77KB)
Self-similar blow-up patterns for a reaction-diffusion equation with weighted reaction in general dimension
Razvan Gabriel Iagar, Ana Isabel Muñoz and Ariel Sánchez
2021doi: 10.3934/cpaa.2022003 +[Abstract](108) +[HTML](45) +[PDF](524.1KB)
Global generalized solutions of a haptotaxis model describing cancer cells invasion and metastatic spread
Meng Liu and Yuxiang Li
2021doi: 10.3934/cpaa.2022004 +[Abstract](65) +[HTML](27) +[PDF](177.39KB)
Inertial manifolds for parabolic differential equations: The fully nonautonomous case
Nguyen Thieu Huy, Pham Truong Xuan, Vu Thi Ngoc Ha and Vu Thi Thuy Ha
2021doi: 10.3934/cpaa.2022005 +[Abstract](112) +[HTML](31) +[PDF](167.32KB)
Global regularity estimates for Neumann problems of elliptic operators with coefficients having a BMO anti-symmetric part in NTA domains
Sibei Yang, Dachun Yang and Wenxian Ma
2021doi: 10.3934/cpaa.2022006 +[Abstract](87) +[HTML](37) +[PDF](323.97KB)
Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities
Thierry Horsin and Mohamed Ali Jendoubi
2021doi: 10.3934/cpaa.2022007 +[Abstract](85) +[HTML](34) +[PDF](1086.02KB)
Monotonicity and symmetry of positive solutions to degenerate quasilinear elliptic systems in half-spaces and strips
Phuong Le and Hoang-Hung Vo
2021doi: 10.3934/cpaa.2022008 +[Abstract](167) +[HTML](32) +[PDF](202.95KB)
Higher P-symmetric Ekeland-Hofer capacities
Kun Shi and Guangcun Lu
2021doi: 10.3934/cpaa.2022009 +[Abstract](70) +[HTML](23) +[PDF](231.91KB)
Existence of solutions for a class of quasilinear Schrödinger equation with a Kirchhoff-type
Die Hu, Xianhua Tang and Qi Zhang
2021doi: 10.3934/cpaa.2022010 +[Abstract](67) +[HTML](27) +[PDF](220.95KB)
Uniform approximation property of frames with applications to erasure recovery
Ting Chen, Fusheng Lv and Wenchang Sun
2021doi: 10.3934/cpaa.2022011 +[Abstract](72) +[HTML](26) +[PDF](158.05KB)
Asymptotic analysis for the electric field concentration with geometry of the core-shell structure
Zhiwen Zhao
2021doi: 10.3934/cpaa.2022012 +[Abstract](82) +[HTML](24) +[PDF](323.42KB)
Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type
Jan-Phillip Bäcker and Matthias Röger
2021doi: 10.3934/cpaa.2022013 +[Abstract](76) +[HTML](34) +[PDF](182.35KB)
Concentration of bound states for fractional Schrödinger-Poisson system via penalization methods
Kaimin Teng and Xian Wu
2021doi: 10.3934/cpaa.2022014 +[Abstract](66) +[HTML](28) +[PDF](258.77KB)
On deterministic solutions for multi-marginal optimal transport with Coulomb cost
Ugo Bindini, Luigi De Pascale and Anna Kausamo
2021doi: 10.3934/cpaa.2022015 +[Abstract](58) +[HTML](32) +[PDF](244.56KB)
On Asymptotic Properties of Semi-relativistic Hartree Equation with combined Hartree-type nonlinearities
Qingxuan Wang, Binhua Feng, Yuan Li and Qihong Shi
2021doi: 10.3934/cpaa.2022017 +[Abstract](69) +[HTML](37) +[PDF](220.96KB)
On spectral gaps of growth-fragmentation semigroups with mass loss or death
Mustapha Mokhtar-Kharroubi
2022doi: 10.3934/cpaa.2022019 +[Abstract](9) +[HTML](5) +[PDF](260.07KB)
On the critical Schrödinger-Poisson system with $ p $-Laplacian
Yao Du, Jiabao Su and Cong Wang
2022doi: 10.3934/cpaa.2022020 +[Abstract](20) +[HTML](7) +[PDF](174.44KB)
The duality method for mean field games systems
Lucio Boccardo and Luigi Orsina
2022doi: 10.3934/cpaa.2022021 +[Abstract](9) +[HTML](5) +[PDF](186.96KB)
Periodic solution and extinction in a periodic chemostat model with delay in microorganism growth
Ningning Ye, Zengyun Hu and Zhidong Teng
2022doi: 10.3934/cpaa.2022022 +[Abstract](12) +[HTML](5) +[PDF](455.18KB)
Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients
Sergio Polidoro, Annalaura Rebucci and Bianca Stroffolini
2022doi: 10.3934/cpaa.2022023 +[Abstract](72) +[HTML](40) +[PDF](275.93KB)
A general multipurpose interpolation procedure: the magic points
Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera and S. H. Pau
2009, 8(1) : 383-404 doi: 10.3934/cpaa.2009.8.383 +[Abstract](6087) +[PDF](826.7KB) Cited By(107)
On the stationary solutions of generalized reaction diffusion equations with $p\& q$-Laplacian
L. Cherfils and Y. Il'yasov
2005, 4(1) : 9-22 doi: 10.3934/cpaa.2005.4.9 +[Abstract](3924) +[PDF](225.5KB) Cited By(106)
Almost periodicity analysis for a delayed Nicholson's blowflies model with nonlinear density-dependent mortality term
Chuangxia Huang, Hua Zhang and Lihong Huang
2019, 18(6) : 3337-3349 doi: 10.3934/cpaa.2019150 +[Abstract](4132) +[HTML](244) +[PDF](373.99KB) Cited By(102)
A Brezis-Nirenberg result for non-local critical equations in low dimension
Raffaella Servadei and Enrico Valdinoci
2013, 12(6) : 2445-2464 doi: 10.3934/cpaa.2013.12.2445 +[Abstract](5578) +[PDF](509.5KB) Cited By(93)
Convergence of generalized proximal point algorithms
Giuseppe Marino and Hong-Kun Xu
2004, 3(4) : 791-808 doi: 10.3934/cpaa.2004.3.791 +[Abstract](5280) +[PDF](181.7KB) Cited By(90)
Periodic solutions of nonlinear periodic differential systems with a small parameter
Adriana Buică, Jean–Pierre Françoise and Jaume Llibre
2007, 6(1) : 103-111 doi: 10.3934/cpaa.2007.6.103 +[Abstract](3154) +[PDF](130.3KB) Cited By(79)
The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system$^*$
Lihui Guo, Wancheng Sheng and Tong Zhang
2010, 9(2) : 431-458 doi: 10.3934/cpaa.2010.9.431 +[Abstract](5208) +[PDF](1276.3KB) Cited By(72)
Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations
Juncheng Wei and Wei Yao
2012, 11(3) : 1003-1011 doi: 10.3934/cpaa.2012.11.1003 +[Abstract](3844) +[PDF](366.4KB) Cited By(69)
A Liouville type Theorem for an integral system
Dezhong Chen and Li Ma
2006, 5(4) : 855-859 doi: 10.3934/cpaa.2006.5.855 +[Abstract](4429) +[PDF](102.3KB) Cited By(69)
On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
Gianni Gilardi, A. Miranville and Giulio Schimperna
2009, 8(3) : 881-912 doi: 10.3934/cpaa.2009.8.881 +[Abstract](4361) +[PDF](395.6KB) Cited By(69)
Error analysis of a conservative finite-element approximation for the Keller-Segel system of chemotaxis
Norikazu Saito
2012, 11(1) : 339-364 doi: 10.3934/cpaa.2012.11.339 +[Abstract](4981) +[PDF](486.1KB) PDF Downloads(914)
Bifurcation and stability of a two-species diffusive Lotka-Volterra model
Li Ma and Shangjiang Guo
2020, 19(3) : 1205-1232 doi: 10.3934/cpaa.2020056 +[Abstract](2732) +[HTML](89) +[PDF](419.64KB) PDF Downloads(895)
Mean value properties and unique continuation
José G. Llorente
2015, 14(1) : 185-199 doi: 10.3934/cpaa.2015.14.185 +[Abstract](3155) +[PDF](427.4KB) PDF Downloads(818)
The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality
Apala Majumdar
2012, 11(3) : 1303-1337 doi: 10.3934/cpaa.2012.11.1303 +[Abstract](3410) +[PDF](596.9KB) PDF Downloads(740)
Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity
Xiumei Deng and Jun Zhou
2020, 19(2) : 923-939 doi: 10.3934/cpaa.2020042 +[Abstract](2957) +[HTML](112) +[PDF](356.11KB) PDF Downloads(610)
W1, p-estimates for elliptic equations with lower order terms
Byungsoo Kang and Hyunseok Kim
2017, 16(3) : 799-822 doi: 10.3934/cpaa.2017038 +[Abstract](3017) +[HTML](134) +[PDF](491.2KB) PDF Downloads(577)
Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression
Lucian Coroianu, Danilo Costarelli, Sorin G. Gal and Gianluca Vinti
2020, 19(8) : 4213-4225 doi: 10.3934/cpaa.2020189 +[Abstract](1536) +[HTML](89) +[PDF](414.25KB) PDF Downloads(539)
On a delayed epidemic model with non-instantaneous impulses
Liang Bai, Juan J. Nieto and José M. Uzal
2020, 19(4) : 1915-1930 doi: 10.3934/cpaa.2020084 +[Abstract](2040) +[HTML](170) +[PDF](356.02KB) PDF Downloads(530)
Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up
Yanbing Yang and Runzhang Xu
2019, 18(3) : 1351-1358 doi: 10.3934/cpaa.2019065 +[Abstract](4959) +[HTML](375) +[PDF](342.33KB) PDF Downloads(527)
Kirchhoff type equations with strong singularities
Yijing Sun and Yuxin Tan
2019, 18(1) : 181-193 doi: 10.3934/cpaa.2019010 +[Abstract](4600) +[HTML](218) +[PDF](342.2KB) PDF Downloads(517)

2020 Impact Factor: 1.916
5 Year Impact Factor: 1.510
2020 CiteScore: 1.9




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