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Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions
Longterm dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent
1.  Department of Mechanics and Mathematics, Kharkov National University, Kharkov, 61077 
2.  Department of Mathematics, University of Virginia, Charlottesville, VA 22903 
3.  Department of Mathematics, University of NebraskaLincoln, Lincoln, NE 68588, United States 
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Xinyu Mei, Yangmin Xiong, Chunyou Sun. Pullback attractor for a weakly damped wave equation with supcubic nonlinearity. Discrete & Continuous Dynamical Systems  A, 2021, 41 (2) : 569600. doi: 10.3934/dcds.2020270 
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Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020345 
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Oussama Landoulsi. Construction of a solitary wave solution of the nonlinear focusing schrödinger equation outside a strictly convex obstacle in the $ L^2 $supercritical case. Discrete & Continuous Dynamical Systems  A, 2021, 41 (2) : 701746. doi: 10.3934/dcds.2020298 
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Youshan Tao, Michael Winkler. Critical mass for infinitetime blowup in a haptotaxis system with nonlinear zeroorder interaction. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 439454. doi: 10.3934/dcds.2020216 
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Omid Nikan, Seyedeh Mahboubeh MolaviArabshai, Hossein Jafari. Numerical simulation of the nonlinear fractional regularized longwave model arising in ion acoustic plasma waves. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020466 
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Ahmad Z. Fino, Wenhui Chen. A global existence result for twodimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 53875411. doi: 10.3934/cpaa.2020243 
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Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 15031528. doi: 10.3934/era.2020079 
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Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Kleingordon equation. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020448 
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Tommi Brander, Joonas Ilmavirta, Petteri Piiroinen, Teemu Tyni. Optimal recovery of a radiating source with multiple frequencies along one line. Inverse Problems & Imaging, 2020, 14 (6) : 967983. doi: 10.3934/ipi.2020044 
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Kihoon Seong. Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2020, 19 (12) : 54375473. doi: 10.3934/cpaa.2020247 
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José Luis López. A quantum approach to KellerSegel dynamics via a dissipative nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020376 
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Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449465. doi: 10.3934/cpaa.2020276 
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Alex H. Ardila, Mykael Cardoso. Blowup solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101119. doi: 10.3934/cpaa.2020259 
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Hua Qiu, ZhengAn Yao. The regularized Boussinesq equations with partial dissipations in dimension two. Electronic Research Archive, 2020, 28 (4) : 13751393. doi: 10.3934/era.2020073 
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Justin Holmer, Chang Liu. Blowup for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blowup profiles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 215242. doi: 10.3934/cpaa.2020264 
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Adel M. AlMahdi, Mohammad M. AlGharabli, Salim A. Messaoudi. New general decay result for a system of viscoelastic wave equations with past history. Communications on Pure & Applied Analysis, 2021, 20 (1) : 389404. doi: 10.3934/cpaa.2020273 
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Annegret Glitzky, Matthias Liero, Grigor Nika. Dimension reduction of thermistor models for largearea organic lightemitting diodes. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020460 
2019 Impact Factor: 1.338
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