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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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Compactness of the complex Green operator on non-pseudoconvex CR manifolds
Joel Coacalle and Andrew Raich
2021, 20(6) : 2139-2154 doi: 10.3934/cpaa.2021061 +[Abstract](219) +[HTML](115) +[PDF](388.09KB)
A new Hodge operator in discrete exterior calculus. Application to fluid mechanics
Rama Ayoub, Aziz Hamdouni and Dina Razafindralandy
2021, 20(6) : 2155-2185 doi: 10.3934/cpaa.2021062 +[Abstract](207) +[HTML](111) +[PDF](3665.16KB)
Orbital stability and spectral properties of solitary waves of Klein–Gordon equation with concentrated nonlinearity
Andrew Comech and Elena Kopylova
2021, 20(6) : 2187-2209 doi: 10.3934/cpaa.2021063 +[Abstract](208) +[HTML](98) +[PDF](433.52KB)
Boundedness and asymptotic stability in a quasilinear two-species chemotaxis system with nonlinear signal production
Xu Pan and Liangchen Wang
2021, 20(6) : 2211-2236 doi: 10.3934/cpaa.2021064 +[Abstract](213) +[HTML](104) +[PDF](435.25KB)
Positive solutions for Choquard equation in exterior domains
Peng Chen and Xiaochun Liu
2021, 20(6) : 2237-2256 doi: 10.3934/cpaa.2021065 +[Abstract](236) +[HTML](95) +[PDF](376.96KB)
Fractional oscillon equations; solvability and connection with classical oscillon equations
Flank D. M. Bezerra, Rodiak N. Figueroa-López and Marcelo J. D. Nascimento
2021, 20(6) : 2257-2277 doi: 10.3934/cpaa.2021067 +[Abstract](243) +[HTML](107) +[PDF](442.93KB)
Local existence and uniqueness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics
Fabio Sperotto Bemfica, Marcelo Mendes Disconzi, Casey Rodriguez and Yuanzhen Shao
2021, 20(6) : 2279-2290 doi: 10.3934/cpaa.2021069 +[Abstract](198) +[HTML](127) +[PDF](347.17KB)
Least energy sign-changing solutions for Schrödinger-Poisson system with critical growth
Xiaoping Chen and Chunlei Tang
2021, 20(6) : 2291-2312 doi: 10.3934/cpaa.2021077 +[Abstract](133) +[HTML](52) +[PDF](411.88KB)
Uniqueness and sign properties of minimizers in a quasilinear indefinite problem
Uriel Kaufmann, Humberto Ramos Quoirin and Kenichiro Umezu
2021, 20(6) : 2313-2322 doi: 10.3934/cpaa.2021078 +[Abstract](106) +[HTML](45) +[PDF](336.94KB)
On local solvability for a class of generalized Mizohata equations
L. R. Nunes and J. R. Dos Santos Filho
2021, 20(6) : 2323-2340 doi: 10.3934/cpaa.2021081 +[Abstract](108) +[HTML](55) +[PDF](363.88KB)
An optimal osmotic control problem for a concrete dam system
Renzhao Chen and Xuezhang Hou
2021, 20(6) : 2341-2359 doi: 10.3934/cpaa.2021082 +[Abstract](84) +[HTML](46) +[PDF](975.67KB)
A class of the non-degenerate complex quotient equations on compact Kähler manifolds
Jundong Zhou
2021, 20(6) : 2361-2377 doi: 10.3934/cpaa.2021085 +[Abstract](106) +[HTML](63) +[PDF](351.87KB)
Asymptotics for the concentrated field between closely located hard inclusions in all dimensions
Zhiwen Zhao and Xia Hao
2021, 20(6) : 2379-2398 doi: 10.3934/cpaa.2021086 +[Abstract](126) +[HTML](44) +[PDF](418.44KB)
Density functions of distribution dependent SDEs driven by Lévy noises
Yulin Song
2021, 20(6) : 2399-2419 doi: 10.3934/cpaa.2021087 +[Abstract](104) +[HTML](59) +[PDF](380.86KB)
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](86) +[HTML](58) +[PDF](319.8KB)
Blow-up results for effectively damped wave models with nonlinear memory
Tayeb Hadj Kaddour and Michael Reissig
2020doi: 10.3934/cpaa.2020239 +[Abstract](841) +[HTML](354) +[PDF](338.09KB)
Remark on 3-D Navier-Stokes system with strong dissipation in one direction
Yanlin Liu and Ping Zhang
2020doi: 10.3934/cpaa.2020244 +[Abstract](687) +[HTML](313) +[PDF](383.55KB)
The two-component Novikov-type systems with peaked solutions and $ H^1 $-conservation law
Min Zhao and Changzheng Qu
2020doi: 10.3934/cpaa.2020245 +[Abstract](743) +[HTML](346) +[PDF](367.37KB)
Multiple solutions for nonlinear cone degenerate elliptic equations
Hua Chen and Yawei Wei
2020doi: 10.3934/cpaa.2020272 +[Abstract](622) +[HTML](262) +[PDF](319.1KB)
Kuramoto order parameters and phase concentration for the Kuramoto-Sakaguchi equation with frustration
Seung-Yeal Ha, Javier Morales and Yinglong Zhang
2021doi: 10.3934/cpaa.2021013 +[Abstract](346) +[HTML](182) +[PDF](496.32KB)
Global solutions of a two-dimensional Riemann problem for the pressure gradient system
Gui-Qiang G. Chen, Qin Wang and Shengguo Zhu
2021doi: 10.3934/cpaa.2021014 +[Abstract](338) +[HTML](212) +[PDF](643.44KB)
On a supersonic-sonic patch arising from the frankl problem in transonic flows
Yanbo Hu and Jiequan Li
2021doi: 10.3934/cpaa.2021015 +[Abstract](284) +[HTML](171) +[PDF](463.0KB)
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](215) +[HTML](122) +[PDF](317.63KB)
Collective behaviors of the Lohe Hermitian sphere model with inertia
Seung-Yeal Ha, Myeongju Kang and Hansol Park
2021doi: 10.3934/cpaa.2021046 +[Abstract](228) +[HTML](105) +[PDF](370.69KB)
Subellipticity of some complex vector fields related to the Witten Laplacian
Wei Xi Li and Chao Jiang Xu
2021doi: 10.3934/cpaa.2021047 +[Abstract](219) +[HTML](104) +[PDF](329.69KB)
Radon measure solutions for steady compressible hypersonic-limit Euler flows passing cylindrically symmetric conical bodies
Yunjuan Jin, Aifang Qu and Hairong Yuan
2021doi: 10.3934/cpaa.2021048 +[Abstract](260) +[HTML](197) +[PDF](449.68KB)
Nonlinear stability of rarefaction waves for a hyperbolic system with Cattaneo's law
Yinsong Bai, Lin He and Huijiang Zhao
2021doi: 10.3934/cpaa.2021049 +[Abstract](214) +[HTML](111) +[PDF](440.73KB)
Uniqueness of steady 1-D shock solutions in a finite nozzle via vanishing viscosity aguments
Beixiang Fang and Qin Zhao
2021doi: 10.3934/cpaa.2021066 +[Abstract](160) +[HTML](97) +[PDF](328.2KB)
Local well-posedness in Sobolev spaces for first-order barotropic causal relativistic viscous hydrodynamics
Fabio S. Bemfica, Marcelo M. Disconzi and P. Jameson Graber
2021doi: 10.3934/cpaa.2021068 +[Abstract](65) +[HTML](30) +[PDF](459.88KB)
A degenerate elliptic problem from subsonic-sonic flows in convergent nozzles
Guanming Gai, Yuanyuan Nie and Chunpeng Wang
2021doi: 10.3934/cpaa.2021070 +[Abstract](211) +[HTML](96) +[PDF](362.63KB)
On the Calderon-Zygmund property of Riesz-transform type operators arising in nonlocal equations
Sasikarn Yeepo, Wicharn Lewkeeratiyutkul, Sujin Khomrutai and Armin Schikorra
2021doi: 10.3934/cpaa.2021071 +[Abstract](70) +[HTML](36) +[PDF](408.68KB)
Remarks on global weak solutions to a two-fluid type model
Huanyao Wen and Changjiang Zhu
2021doi: 10.3934/cpaa.2021072 +[Abstract](126) +[HTML](66) +[PDF](374.64KB)
Uniform regularity and vanishing viscosity limit for the incompressible non-resistive MHD system with transverse magnetic field
Cheng-Jie Liu, Feng Xie and Tong Yang
2021doi: 10.3934/cpaa.2021073 +[Abstract](139) +[HTML](71) +[PDF](366.64KB)
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](134) +[HTML](66) +[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](134) +[HTML](78) +[PDF](782.03KB)
Hadamard Semidifferential, Oriented Distance Function, and some Applications
Michel C. Delfour
2021doi: 10.3934/cpaa.2021076 +[Abstract](178) +[HTML](92) +[PDF](482.37KB)
Three-dimensional supersonic flows of Euler-Poisson system for potential flow
Myoungjean Bae and Hyangdong Park
2021doi: 10.3934/cpaa.2021079 +[Abstract](155) +[HTML](61) +[PDF](369.42KB)
Large-time behaviors of the solution to 3D compressible Navier-Stokes equations in half space with Navier boundary conditions
Teng Wang and Yi Wang
2021doi: 10.3934/cpaa.2021080 +[Abstract](134) +[HTML](66) +[PDF](371.21KB)
On the stability of two-dimensional nonisentropic elastic vortex sheets
Robin Ming Chen, Feimin Huang, Dehua Wang and Difan Yuan
2021doi: 10.3934/cpaa.2021083 +[Abstract](125) +[HTML](71) +[PDF](307.28KB)
On the invariant region for compressible Euler equations with a general equation of state
Hailiang Liu and Ferdinand Thein
2021doi: 10.3934/cpaa.2021084 +[Abstract](160) +[HTML](73) +[PDF](281.36KB)
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](104) +[HTML](106) +[PDF](468.47KB)
The curved symmetric $ 2 $– and $ 3 $–center problem on constant negative surfaces
Sawsan Alhowaity, Ernesto Pérez-Chavela and Juan Manuel Sánchez-Cerritos
2021doi: 10.3934/cpaa.2021090 +[Abstract](83) +[HTML](24) +[PDF](671.3KB)
Improved well-posedness results for the Maxwell-Klein-Gordon system in 2D
Hartmut Pecher
2021doi: 10.3934/cpaa.2021091 +[Abstract](48) +[HTML](24) +[PDF](408.71KB)
Stability results of a singular local interaction elastic/viscoelastic coupled wave equations with time delay
Mohammad Akil, Haidar Badawi and Ali Wehbe
2021doi: 10.3934/cpaa.2021092 +[Abstract](51) +[HTML](19) +[PDF](453.3KB)
Data-driven optimal control of a seir model for COVID-19
Hailiang Liu and Xuping Tian
2021doi: 10.3934/cpaa.2021093 +[Abstract](56) +[HTML](42) +[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](51) +[HTML](39) +[PDF](1366.37KB)
On the hot spots of quantum graphs
James B. Kennedy and Jonathan Rohleder
2021doi: 10.3934/cpaa.2021095 +[Abstract](63) +[HTML](26) +[PDF](452.6KB)
Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions
Jie Yang and Haibo Chen
2021doi: 10.3934/cpaa.2021096 +[Abstract](61) +[HTML](22) +[PDF](413.2KB)
On the stability of boundary equilibria in Filippov systems
D. J. W. Simpson
2021doi: 10.3934/cpaa.2021097 +[Abstract](62) +[HTML](28) +[PDF](594.7KB)
Boundary stabilization of non-diagonal systems by proportional feedback forms
Ionuţ Munteanu
2021doi: 10.3934/cpaa.2021098 +[Abstract](42) +[HTML](16) +[PDF](325.56KB)
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](5267) +[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](3302) +[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](3241) +[HTML](235) +[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](4833) +[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](4487) +[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](2573) +[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](4470) +[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](3175) +[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](3853) +[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](3680) +[PDF](395.6KB) Cited By(69)
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](2171) +[HTML](84) +[PDF](419.64KB) PDF Downloads(570)
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](4001) +[PDF](486.1KB) PDF Downloads(499)
Mean value properties and unique continuation
José G. Llorente
2015, 14(1) : 185-199 doi: 10.3934/cpaa.2015.14.185 +[Abstract](2636) +[PDF](427.4KB) PDF Downloads(475)
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](2288) +[HTML](103) +[PDF](356.11KB) PDF Downloads(407)
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](4367) +[HTML](370) +[PDF](342.33KB) PDF Downloads(403)
Coupled systems of Hilfer fractional differential inclusions in banach spaces
Saïd Abbas, Mouffak Benchohra and John R. Graef
2018, 17(6) : 2479-2493 doi: 10.3934/cpaa.2018118 +[Abstract](4823) +[HTML](224) +[PDF](328.43KB) PDF Downloads(401)
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](885) +[HTML](85) +[PDF](414.25KB) PDF Downloads(396)
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](2820) +[PDF](596.9KB) PDF Downloads(391)
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](1395) +[HTML](167) +[PDF](356.02KB) PDF Downloads(376)
Kirchhoff type equations with strong singularities
Yijing Sun and Yuxin Tan
2019, 18(1) : 181-193 doi: 10.3934/cpaa.2019010 +[Abstract](4149) +[HTML](212) +[PDF](342.2KB) PDF Downloads(374)

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