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$L^p$ Estimates for the wave equation with the inverse-square potential
| 1. | Laboratoire d'Analyse Numérique, URA CNRS 189, Université Pierre et Marie Curie, 175 rue Chevaleret, 75252 Paris, France |
| 2. | Department of Mathematics, Princeton University, Princeton N.J. 08544, United States |
| 3. | Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway NJ 08854, United States |
| [1] |
Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh. Dispersive estimate for the wave equation with the inverse-square potential. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1387-1400. doi: 10.3934/dcds.2003.9.1387 |
| [2] |
Hyeongjin Lee, Ihyeok Seo, Jihyeon Seok. Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 597-608. doi: 10.3934/dcds.2020024 |
| [3] |
Gisèle Ruiz Goldstein, Jerome A. Goldstein, Abdelaziz Rhandi. Kolmogorov equations perturbed by an inverse-square potential. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 623-630. doi: 10.3934/dcdss.2011.4.623 |
| [4] |
Umberto Biccari. Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential. Mathematical Control and Related Fields, 2019, 9 (1) : 191-219. doi: 10.3934/mcrf.2019011 |
| [5] |
Jinmyong An, Roesong Jang, Jinmyong Kim. Global existence and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022111 |
| [6] |
Yaoping Chen, Jianqing Chen. Existence of multiple positive weak solutions and estimates for extremal values for a class of concave-convex elliptic problems with an inverse-square potential. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1531-1552. doi: 10.3934/cpaa.2017073 |
| [7] |
Rowan Killip, Changxing Miao, Monica Visan, Junyong Zhang, Jiqiang Zheng. The energy-critical NLS with inverse-square potential. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3831-3866. doi: 10.3934/dcds.2017162 |
| [8] |
Kazuhiro Ishige, Asato Mukai. Large time behavior of solutions of the heat equation with inverse square potential. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 4041-4069. doi: 10.3934/dcds.2018176 |
| [9] |
Toshiyuki Suzuki. Scattering theory for semilinear Schrödinger equations with an inverse-square potential via energy methods. Evolution Equations and Control Theory, 2019, 8 (2) : 447-471. doi: 10.3934/eect.2019022 |
| [10] |
Hengguang Li, Jeffrey S. Ovall. A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1377-1391. doi: 10.3934/dcdsb.2015.20.1377 |
| [11] |
Toshiyuki Suzuki. Nonlinear Schrödinger equations with inverse-square potentials in two dimensional space. Conference Publications, 2015, 2015 (special) : 1019-1024. doi: 10.3934/proc.2015.1019 |
| [12] |
Patrick Martinez, Judith Vancostenoble. The cost of boundary controllability for a parabolic equation with inverse square potential. Evolution Equations and Control Theory, 2019, 8 (2) : 397-422. doi: 10.3934/eect.2019020 |
| [13] |
Montgomery Taylor. The diffusion phenomenon for damped wave equations with space-time dependent coefficients. Discrete and Continuous Dynamical Systems, 2018, 38 (11) : 5921-5941. doi: 10.3934/dcds.2018257 |
| [14] |
Daniel G. Alfaro Vigo, Amaury C. Álvarez, Grigori Chapiro, Galina C. García, Carlos G. Moreira. Solving the inverse problem for an ordinary differential equation using conjugation. Journal of Computational Dynamics, 2020, 7 (2) : 183-208. doi: 10.3934/jcd.2020008 |
| [15] |
Veronica Felli, Ana Primo. Classification of local asymptotics for solutions to heat equations with inverse-square potentials. Discrete and Continuous Dynamical Systems, 2011, 31 (1) : 65-107. doi: 10.3934/dcds.2011.31.65 |
| [16] |
Toshiyuki Suzuki. Energy methods for Hartree type equations with inverse-square potentials. Evolution Equations and Control Theory, 2013, 2 (3) : 531-542. doi: 10.3934/eect.2013.2.531 |
| [17] |
Kazuhiro Ishige, Yujiro Tateishi. Decay estimates for Schrödinger heat semigroup with inverse square potential in Lorentz spaces II. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 369-401. doi: 10.3934/dcds.2021121 |
| [18] |
Dong-Ho Tsai, Chia-Hsing Nien. On space-time periodic solutions of the one-dimensional heat equation. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3997-4017. doi: 10.3934/dcds.2020037 |
| [19] |
Suna Ma, Huiyuan Li, Zhimin Zhang. Novel spectral methods for Schrödinger equations with an inverse square potential on the whole space. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1589-1615. doi: 10.3934/dcdsb.2018221 |
| [20] |
Xiaopeng Zhao. Space-time decay estimates of solutions to liquid crystal system in $\mathbb{R}^3$. Communications on Pure and Applied Analysis, 2019, 18 (1) : 1-13. doi: 10.3934/cpaa.2019001 |
2021 Impact Factor: 1.588
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