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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 & Continuous Dynamical Systems - A, 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 & Continuous Dynamical Systems - A, 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 & 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 & Related Fields, 2019, 9 (1) : 191-219. doi: 10.3934/mcrf.2019011 |
[5] |
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 & Applied Analysis, 2017, 16 (5) : 1531-1552. doi: 10.3934/cpaa.2017073 |
[6] |
Rowan Killip, Changxing Miao, Monica Visan, Junyong Zhang, Jiqiang Zheng. The energy-critical NLS with inverse-square potential. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3831-3866. doi: 10.3934/dcds.2017162 |
[7] |
Kazuhiro Ishige, Asato Mukai. Large time behavior of solutions of the heat equation with inverse square potential. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 4041-4069. doi: 10.3934/dcds.2018176 |
[8] |
Hengguang Li, Jeffrey S. Ovall. A posteriori eigenvalue error estimation for a Schrödinger operator with inverse square potential. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1377-1391. doi: 10.3934/dcdsb.2015.20.1377 |
[9] |
Toshiyuki Suzuki. Scattering theory for semilinear Schrödinger equations with an inverse-square potential via energy methods. Evolution Equations & Control Theory, 2019, 8 (2) : 447-471. doi: 10.3934/eect.2019022 |
[10] |
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 |
[11] |
Patrick Martinez, Judith Vancostenoble. The cost of boundary controllability for a parabolic equation with inverse square potential. Evolution Equations & Control Theory, 2019, 8 (2) : 397-422. doi: 10.3934/eect.2019020 |
[12] |
Montgomery Taylor. The diffusion phenomenon for damped wave equations with space-time dependent coefficients. Discrete & Continuous Dynamical Systems - A, 2018, 38 (11) : 5921-5941. doi: 10.3934/dcds.2018257 |
[13] |
Veronica Felli, Ana Primo. Classification of local asymptotics for solutions to heat equations with inverse-square potentials. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 65-107. doi: 10.3934/dcds.2011.31.65 |
[14] |
Toshiyuki Suzuki. Energy methods for Hartree type equations with inverse-square potentials. Evolution Equations & Control Theory, 2013, 2 (3) : 531-542. doi: 10.3934/eect.2013.2.531 |
[15] |
Suna Ma, Huiyuan Li, Zhimin Zhang. Novel spectral methods for Schrödinger equations with an inverse square potential on the whole space. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1589-1615. doi: 10.3934/dcdsb.2018221 |
[16] |
Dong-Ho Tsai, Chia-Hsing Nien. On space-time periodic solutions of the one-dimensional heat equation. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020037 |
[17] |
Norisuke Ioku. Some space-time integrability estimates of the solution for heat equations in two dimensions. Conference Publications, 2011, 2011 (Special) : 707-716. doi: 10.3934/proc.2011.2011.707 |
[18] |
Xiaopeng Zhao. Space-time decay estimates of solutions to liquid crystal system in $\mathbb{R}^3$. Communications on Pure & Applied Analysis, 2019, 18 (1) : 1-13. doi: 10.3934/cpaa.2019001 |
[19] |
Xiaoyan Lin, Yubo He, Xianhua Tang. Existence and asymptotic behavior of ground state solutions for asymptotically linear Schrödinger equation with inverse square potential. Communications on Pure & Applied Analysis, 2019, 18 (3) : 1547-1565. doi: 10.3934/cpaa.2019074 |
[20] |
Yanzhao Cao, Li Yin. Spectral Galerkin method for stochastic wave equations driven by space-time white noise. Communications on Pure & Applied Analysis, 2007, 6 (3) : 607-617. doi: 10.3934/cpaa.2007.6.607 |
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