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Communications on Pure and 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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On the attractor for a semilinear wave equation with variable coefficients and nonlinear boundary dissipation
Jiacheng Wang and Peng-Fei Yao
2022, 21(6) : 1857-1871 doi: 10.3934/cpaa.2021043 +[Abstract](1083) +[HTML](497) +[PDF](390.4KB)
Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations
Juan Wen, Yaling He, Yinnian He and Kun Wang
2022, 21(6) : 1873-1894 doi: 10.3934/cpaa.2021074 +[Abstract](1062) +[HTML](473) +[PDF](1705.66KB)
On the even solutions of the Toda system: A degree argument approach
Yong Liu, Jing Tian and Xuelin Yong
2022, 21(6) : 1895-1916 doi: 10.3934/cpaa.2021075 +[Abstract](915) +[HTML](439) +[PDF](841.33KB)
Hadamard Semidifferential, Oriented Distance Function, and some Applications
Michel C. Delfour
2022, 21(6) : 1917-1951 doi: 10.3934/cpaa.2021076 +[Abstract](1031) +[HTML](443) +[PDF](591.28KB)
Ground state solutions for the fractional problems with dipole-type potential and critical exponent
Yu Su and Zhaosheng Feng
2022, 21(6) : 1953-1968 doi: 10.3934/cpaa.2021111 +[Abstract](755) +[HTML](394) +[PDF](394.34KB)
An indirect BIE free of degenerate scales
Jeng-Tzong Chen, Shing-Kai Kao, Jeng-Hong Kao and Wei-Chen Tai
2022, 21(6) : 1969-1985 doi: 10.3934/cpaa.2021114 +[Abstract](795) +[HTML](348) +[PDF](1665.55KB)
Dynamics of solitary waves and periodic waves for a generalized KP-MEW-Burgers equation with damping
Zengji Du, Xiaojie Lin and Yulin Ren
2022, 21(6) : 1987-2003 doi: 10.3934/cpaa.2021118 +[Abstract](644) +[HTML](411) +[PDF](423.07KB)
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
2022, 21(6) : 2005-2034 doi: 10.3934/cpaa.2021145 +[Abstract](777) +[HTML](383) +[PDF](506.42KB)
Controllability and stabilization of gravity-capillary surface water waves in a basin
Jing Cui, Guangyue Gao and Shu-Ming Sun
2022, 21(6) : 2035-2063 doi: 10.3934/cpaa.2021158 +[Abstract](580) +[HTML](291) +[PDF](476.02KB)
Instantaneous blow-up for nonlinear Sobolev type equations with potentials on Riemannian manifolds
Mohamed Jleli and Bessem Samet
2022, 21(6) : 2065-2078 doi: 10.3934/cpaa.2022036 +[Abstract](158) +[HTML](57) +[PDF](373.48KB)
Liouville type theorem for Hartree-Fock Equation on half space
Xiaomei Chen and Xiaohui Yu
2022, 21(6) : 2079-2100 doi: 10.3934/cpaa.2022050 +[Abstract](215) +[HTML](93) +[PDF](432.63KB)
Gagliardo-Nirenberg-Sobolev inequalities on planar graphs
Maria J. Esteban
2022, 21(6) : 2101-2114 doi: 10.3934/cpaa.2022051 +[Abstract](184) +[HTML](83) +[PDF](617.33KB)
Multi-dimensional degenerate operators in $L^p$-spaces
Simona Fornaro, Giorgio Metafune, Diego Pallara and Roland Schnaubelt
2022, 21(6) : 2115-2145 doi: 10.3934/cpaa.2022052 +[Abstract](171) +[HTML](83) +[PDF](563.25KB)
A potential approach for planning mean-field games in one dimension
Tigran Bakaryan, Rita Ferreira and Diogo Gomes
2022, 21(6) : 2147-2187 doi: 10.3934/cpaa.2022054 +[Abstract](170) +[HTML](72) +[PDF](641.95KB)
Curvature-driven front propagation through planar lattices in oblique directions
Mia Jukić and Hermen Jan Hupkes
2022, 21(6) : 2189-2251 doi: 10.3934/cpaa.2022055 +[Abstract](165) +[HTML](84) +[PDF](1848.51KB)
Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities
Rakesh Arora
2022, 21(6) : 2253-2269 doi: 10.3934/cpaa.2022056 +[Abstract](196) +[HTML](74) +[PDF](437.42KB)
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](850) +[HTML](451) +[PDF](319.8KB)
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](1017) +[HTML](568) +[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](1146) +[HTML](457) +[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](833) +[HTML](558) +[PDF](1366.37KB)
Semi-discrete and fully discrete HDG methods for Burgers' equation
Zimo Zhu, Gang Chen and Xiaoping Xie
2021doi: 10.3934/cpaa.2021132 +[Abstract](735) +[HTML](402) +[PDF](488.08KB)
Dynamical analysis in disease transmission and final epidemic size
Daifeng Duan, Cuiping Wang and Yuan Yuan
2021doi: 10.3934/cpaa.2021150 +[Abstract](653) +[HTML](297) +[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](825) +[HTML](328) +[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](643) +[HTML](287) +[PDF](1835.77KB)
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](663) +[HTML](421) +[PDF](2334.82KB)
Hamiltonian description of internal ocean waves with Coriolis force
Joseph D. Cullen and Rossen I. Ivanov
2022doi: 10.3934/cpaa.2022029 +[Abstract](318) +[HTML](160) +[PDF](181.83KB)
On the spherical geopotential approximation for Saturn
Susanna V. Haziot
2022doi: 10.3934/cpaa.2022035 +[Abstract](235) +[HTML](112) +[PDF](292.68KB)
The ocean and the atmosphere: An applied mathematician's view
R. S. Johnson
2022doi: 10.3934/cpaa.2022040 +[Abstract](269) +[HTML](83) +[PDF](1403.25KB)
Particle paths in equatorial flows
Tony Lyons
2022doi: 10.3934/cpaa.2022041 +[Abstract](193) +[HTML](81) +[PDF](201.22KB)
On three-dimensional free surface water flows with constant vorticity
Calin I. Martin
2022doi: 10.3934/cpaa.2022053 +[Abstract](200) +[HTML](78) +[PDF](247.73KB)
Energy considerations for nonlinear equatorial water waves
David Henry
2022doi: 10.3934/cpaa.2022057 +[Abstract](161) +[HTML](65) +[PDF](411.26KB)
Multiple localized nodal solutions of high topological type for Kirchhoff-type equation with double potentials
Zhi-Guo Wu, Wen Guan and Da-Bin Wang
2022doi: 10.3934/cpaa.2022058 +[Abstract](155) +[HTML](68) +[PDF](556.05KB)
Wong-Zakai approximations and pathwise dynamics of stochastic fractional lattice systems
Yiju Chen, Xiaohu Wang and Kenan Wu
2022doi: 10.3934/cpaa.2022059 +[Abstract](151) +[HTML](61) +[PDF](546.88KB)
Singular quasilinear critical Schrödinger equations in $ \mathbb {R}^N $
Laura Baldelli and Roberta Filippucci
2022doi: 10.3934/cpaa.2022060 +[Abstract](142) +[HTML](59) +[PDF](674.44KB)
Weakly nonlinear waves in stratified shear flows
Anna Geyer and Ronald Quirchmayr
2022doi: 10.3934/cpaa.2022061 +[Abstract](179) +[HTML](77) +[PDF](442.49KB)
Parabolic Systems with measurable coefficients in weighted Sobolev spaces
Doyoon Kim, Kyeong-Hun Kim and Kijung Lee
2022doi: 10.3934/cpaa.2022062 +[Abstract](118) +[HTML](47) +[PDF](517.87KB)
Well-posedness for a coupled system of Kawahara/KdV type equations with polynomials nonlinearities
Cezar Kondo and Ronaldo Pes
2022doi: 10.3934/cpaa.2022063 +[Abstract](108) +[HTML](54) +[PDF](428.98KB)
The surface current of Ekman flows with time-dependent eddy viscosity
Luigi Roberti
2022doi: 10.3934/cpaa.2022064 +[Abstract](141) +[HTML](44) +[PDF](450.67KB)
Wellposedness of a DNA replication model based on a nucleation-growth process
J. Nieto and M. O. Vásquez
2022doi: 10.3934/cpaa.2022065 +[Abstract](93) +[HTML](34) +[PDF](403.66KB)
The Łojasiewicz inequality for free energy functionals on a graph
Kongzhi Li and Xiaoping Xue
2022doi: 10.3934/cpaa.2022066 +[Abstract](112) +[HTML](57) +[PDF](426.95KB)
Exact solution and instability for geophysical edge waves
Fahe Miao, Michal Fečkan and Jinrong Wang
2022doi: 10.3934/cpaa.2022067 +[Abstract](123) +[HTML](49) +[PDF](1898.74KB)
On the solvability of a semilinear higher-order elliptic problem for the vector field method in image registration
Xiaojun Zheng, Zhongdan Huan and Jun Liu
2022doi: 10.3934/cpaa.2022068 +[Abstract](110) +[HTML](46) +[PDF](461.14KB)
The effect of the weight function on the number of nodal solutions of the Kirchhoff-type equations in high dimensions
He Zhang and Haibo Chen
2022doi: 10.3934/cpaa.2022069 +[Abstract](93) +[HTML](34) +[PDF](450.23KB)
Stability, existence and non-existence of $ T $-periodic solutions of nonlinear delayed differential equations with $ \varphi $-Laplacian
Pablo Amster, Mariel Paula Kuna and Dionicio Santos
2022doi: 10.3934/cpaa.2022070 +[Abstract](79) +[HTML](31) +[PDF](369.09KB)
On spectral and fractional powers of damped wave equations
Maykel Belluzi, Flank D. M. Bezerra and Marcelo J. D. Nascimento
2022doi: 10.3934/cpaa.2022071 +[Abstract](102) +[HTML](32) +[PDF](548.94KB)
Global Carleman estimate and its applications for a sixth-order equation related to thin solid films
Yanpeng Jin and Ying Fu
2022doi: 10.3934/cpaa.2022072 +[Abstract](115) +[HTML](29) +[PDF](415.39KB)
Sharp subcritical Sobolev inequalities and uniqueness of nonnegative solutions to high-order Lane-Emden equations on $ \mathbb{S}^n $
Lu Chen, Guozhen Lu and Yansheng Shen
2022doi: 10.3934/cpaa.2022073 +[Abstract](124) +[HTML](36) +[PDF](432.77KB)
Minimisers of Helfrich functional for surfaces of revolution
Huaiyu Jian and Hongbo Zeng
2022doi: 10.3934/cpaa.2022074 +[Abstract](79) +[HTML](26) +[PDF](333.92KB)
Geophysics and Stuart vortices on a sphere meet differential geometry
Łukasz Rudnicki
2022doi: 10.3934/cpaa.2022075 +[Abstract](67) +[HTML](23) +[PDF](418.07KB)
Liouville links and chains on the plane and associated stationary point vortex equilibria
Vikas S. Krishnamurthy
2022doi: 10.3934/cpaa.2022076 +[Abstract](73) +[HTML](27) +[PDF](2446.69KB)
Emergent dynamics of the fractional Cucker-Smale model under general network topologies
Jinwook Jung and Peter Kuchling
2022doi: 10.3934/cpaa.2022077 +[Abstract](76) +[HTML](25) +[PDF](1212.88KB)
Nonexistence of Positive Solutions for high-order Hardy-H$ \acute{e} $non Systems on $ \mathbb{R}^{n} $
Rong Zhang
2022doi: 10.3934/cpaa.2022078 +[Abstract](81) +[HTML](31) +[PDF](408.53KB)
Fourier transform of surface–carried measures of two-dimensional generic surfaces and applications
Jean-Claude Cuenin and Robert Schippa
2022doi: 10.3934/cpaa.2022079 +[Abstract](68) +[HTML](25) +[PDF](456.35KB)
Asymptotic behavior of eigenvalues of the Maxwell system in the presence of small changes in the interface of an inclusion
Abdessatar Khelifi and Siwar Saidani
2022doi: 10.3934/cpaa.2022080 +[Abstract](117) +[HTML](63) +[PDF](486.56KB)
Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity
Zixiao Liu and Jiguang Bao
2022doi: 10.3934/cpaa.2022081 +[Abstract](61) +[HTML](18) +[PDF](464.0KB)
Ground state solutions for asymptotically periodic nonlinearities for Kirchhoff problems
Edcarlos D. Silva and Jefferson S. Silva
2022doi: 10.3934/cpaa.2022082 +[Abstract](79) +[HTML](20) +[PDF](538.48KB)
Stability analysis of the boundary value problem modelling a two-layer ocean
Kateryna Marynets
2022doi: 10.3934/cpaa.2022083 +[Abstract](86) +[HTML](22) +[PDF](625.16KB)
Existence and uniqueness of radial solutions for Hardy-Hénon equations involving k-Hessian operators
Kods Hassine
2022doi: 10.3934/cpaa.2022084 +[Abstract](46) +[HTML](17) +[PDF](373.02KB)
On the nonlinear three-dimensional models in equatorial ocean flows
Biswajit Basu
2022doi: 10.3934/cpaa.2022085 +[Abstract](34) +[HTML](9) +[PDF](2891.73KB)
Plateau-rayleigh instability of singular minimal surfaces
Rafael López
2022doi: 10.3934/cpaa.2022086 +[Abstract](42) +[HTML](25) +[PDF](590.07KB)
Non-convex sweeping processes in the space of regulated functions
Pavel Krejčí, Giselle Antunes Monteiro and Vincenzo Recupero
2022doi: 10.3934/cpaa.2022087 +[Abstract](41) +[HTML](13) +[PDF](537.68KB)
Strongly singular convective elliptic equations in $ \mathbb{R}^N $ driven by a non-homogeneous operator
Laura Gambera and Umberto Guarnotta
2022doi: 10.3934/cpaa.2022088 +[Abstract](39) +[HTML](11) +[PDF](499.33KB)
Hopf's lemmas for parabolic fractional p-Laplacians
Pengyan Wang and Wenxiong Chen
2022doi: 10.3934/cpaa.2022089 +[Abstract](52) +[HTML](14) +[PDF](367.82KB)
Limit cycle bifurcations by perturbing piecewise Hamiltonian systems with a nonregular switching line via multiple parameters
Yuan Chang and Yuzhen Bai
2022doi: 10.3934/cpaa.2022090 +[Abstract](3) +[HTML](0) +[PDF](476.89KB)
Freidlin-Wentzell's large deviation principle for stochastic integral evolution equations
Xiaomin Huang, Yanpei Jiang and Wei Liu
2022doi: 10.3934/cpaa.2022091 +[Abstract](6) +[HTML](5) +[PDF](476.65KB)
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](6665) +[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](4237) +[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](4475) +[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](5990) +[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](5664) +[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](3394) +[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](5601) +[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](4162) +[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](4683) +[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](4751) +[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](5567) +[PDF](486.1KB) PDF Downloads(1177)
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](3017) +[HTML](91) +[PDF](419.64KB) PDF Downloads(1018)
Mean value properties and unique continuation
José G. Llorente
2015, 14(1) : 185-199 doi: 10.3934/cpaa.2015.14.185 +[Abstract](3385) +[PDF](427.4KB) PDF Downloads(968)
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](3862) +[PDF](596.9KB) PDF Downloads(952)
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](3314) +[HTML](113) +[PDF](356.11KB) PDF Downloads(688)
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](3343) +[HTML](134) +[PDF](491.2KB) PDF Downloads(649)
On the Dirichlet boundary value problem for the normalized $p$-laplacian evolution
Agnid Banerjee and Nicola Garofalo
2015, 14(1) : 1-21 doi: 10.3934/cpaa.2015.14.1 +[Abstract](3438) +[PDF](486.2KB) PDF Downloads(606)
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](2390) +[HTML](171) +[PDF](356.02KB) PDF Downloads(598)
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](5202) +[HTML](375) +[PDF](342.33KB) PDF Downloads(569)
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](1782) +[HTML](90) +[PDF](414.25KB) PDF Downloads(567)

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

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