-
Previous Article
A sharp scattering condition for focusing mass-subcritical nonlinear Schrödinger equation
- CPAA Home
- This Issue
-
Next Article
A numerical approach to Blow-up issues for Davey-Stewartson II systems
On the pointwise decay estimate for the wave equation with compactly supported forcing term
1. | Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810 |
References:
[1] |
M. Di Flaviano, Lower bounds of the life span of classical solutions to a system of semilinear wave equations in two space dimensions, J. Math. Anal. Appl., 281 (2003), 22-45. |
[2] |
P. Godin, Long time behavior of solutions to some nonlinear invariant mixed problems, Comm. Partial Differential Equations, 14 (1989), 299-374.
doi: 10.1080/03605308908820599. |
[3] |
P. Godin, Global existence of solutions to some exterior radial quasilinear Cauchy-Dirichlet problems, Amer. J. Math., 117 (1995), 1475-1505.
doi: 10.2307/2375027. |
[4] |
N. Hayashi, Global existence of small solutions to quadratic nonlinear wave equations in an exterior domain, J. Funct. Anal., 131 (1995), 302-344.
doi: 10.1006/jfan.1995.1091. |
[5] |
F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math., 28 (1979), 235-268.
doi: 10.1007/BF01647974. |
[6] |
S. Katayama and H. Kubo, An alternative proof of global existence for nonlinear wave equations in an exterior domain, J. Math. Soc. Japan, 60 (2008), 1135-1170. |
[7] |
S. Katayama, H. Kubo, and S. Lucente, Almost global existence for exterior Neumann problems of semilinear wave equations in 2D, Commun. Pure Appl. Anal., 12 (2013), 2331-2360.
doi: 10.3934/cpaa.2013.12.2331. |
[8] |
M. Keel, H. Smith and C. D. Sogge, Global existence for a quasilinear wave equation outside of star-shaped domains, J. Funct. Anal., 189 (2002), 155-226.
doi: 10.1006/jfan.2001.3844. |
[9] |
M. Keel, H. Smith and C. D. Sogge, Almost global existence for quasilinear wave equations in three space dimensions, J. Amer. Math. Soc., 17 (2004), 109-153.
doi: 10.1090/S0894-0347-03-00443-0. |
[10] |
S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math., 38 (1985), 321-332.
doi: 10.1002/cpa.3160380305. |
[11] |
H. Kubo and K. Kubota, Asymptotic behavior of classical solutions to a system of semilinier wave equations in low space dimensions, J. Math. Soc. Japan, 53 (2001), 875-912.
doi: 10.2969/jmsj/05340875. |
[12] |
H. Kubo, Uniform decay estimates for the wave equation in an exterior domain, in Asymptotic analysis and singularities, 31-54, Advanced Studies in Pure Mathematics 47-1, Math. Soc. of Japan, 2007. |
[13] |
H. Kubo, Global existence for nonlinear wave equations in an exterior domain in 2D, Evolution Equations and Control Theory, 2 (2013), 319-335.
doi: 10.3934/eect.2013.2.319. |
[14] |
H. Kubo, Almost global existence for nonlinear wave equations in an exterior domain in 2D, J. Differential Equations, 257 (2014), 2765-2800. ArXiv: 1204.3725v2.
doi: 10.1016/j.jde.2014.05.048. |
[15] |
K. Kubota, Existence of a global solutions to a semi-linear wave equation with initial data of non-compact support in low space dimensions, Hokkaido Math. J., 22 (1993), 123-180.
doi: 10.14492/hokmj/1381413170. |
[16] |
J. Metcalfe, Global existence for semilinear wave equations exterior to nontrapping obstacles, Houston J. Math., 30 (2004), 259-281. |
[17] |
J. Metcalfe, M. Nakamura and C. D. Sogge, Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition, Japan. J. Math. (N.S.), 31 (2005), 391-472. |
[18] |
J. Metcalfe and C. D. Sogge, Hyperbolic trapped rays and global existence of quasilinear wave equations, Invent. Math., 159 (2005), 75-117.
doi: 10.1007/s00222-004-0383-2. |
[19] |
Y. Shibata and Y. Tsutsumi, On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain, Math. Z., 191 (1986), 165-199.
doi: 10.1007/BF01164023. |
show all references
References:
[1] |
M. Di Flaviano, Lower bounds of the life span of classical solutions to a system of semilinear wave equations in two space dimensions, J. Math. Anal. Appl., 281 (2003), 22-45. |
[2] |
P. Godin, Long time behavior of solutions to some nonlinear invariant mixed problems, Comm. Partial Differential Equations, 14 (1989), 299-374.
doi: 10.1080/03605308908820599. |
[3] |
P. Godin, Global existence of solutions to some exterior radial quasilinear Cauchy-Dirichlet problems, Amer. J. Math., 117 (1995), 1475-1505.
doi: 10.2307/2375027. |
[4] |
N. Hayashi, Global existence of small solutions to quadratic nonlinear wave equations in an exterior domain, J. Funct. Anal., 131 (1995), 302-344.
doi: 10.1006/jfan.1995.1091. |
[5] |
F. John, Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math., 28 (1979), 235-268.
doi: 10.1007/BF01647974. |
[6] |
S. Katayama and H. Kubo, An alternative proof of global existence for nonlinear wave equations in an exterior domain, J. Math. Soc. Japan, 60 (2008), 1135-1170. |
[7] |
S. Katayama, H. Kubo, and S. Lucente, Almost global existence for exterior Neumann problems of semilinear wave equations in 2D, Commun. Pure Appl. Anal., 12 (2013), 2331-2360.
doi: 10.3934/cpaa.2013.12.2331. |
[8] |
M. Keel, H. Smith and C. D. Sogge, Global existence for a quasilinear wave equation outside of star-shaped domains, J. Funct. Anal., 189 (2002), 155-226.
doi: 10.1006/jfan.2001.3844. |
[9] |
M. Keel, H. Smith and C. D. Sogge, Almost global existence for quasilinear wave equations in three space dimensions, J. Amer. Math. Soc., 17 (2004), 109-153.
doi: 10.1090/S0894-0347-03-00443-0. |
[10] |
S. Klainerman, Uniform decay estimates and the Lorentz invariance of the classical wave equation, Comm. Pure Appl. Math., 38 (1985), 321-332.
doi: 10.1002/cpa.3160380305. |
[11] |
H. Kubo and K. Kubota, Asymptotic behavior of classical solutions to a system of semilinier wave equations in low space dimensions, J. Math. Soc. Japan, 53 (2001), 875-912.
doi: 10.2969/jmsj/05340875. |
[12] |
H. Kubo, Uniform decay estimates for the wave equation in an exterior domain, in Asymptotic analysis and singularities, 31-54, Advanced Studies in Pure Mathematics 47-1, Math. Soc. of Japan, 2007. |
[13] |
H. Kubo, Global existence for nonlinear wave equations in an exterior domain in 2D, Evolution Equations and Control Theory, 2 (2013), 319-335.
doi: 10.3934/eect.2013.2.319. |
[14] |
H. Kubo, Almost global existence for nonlinear wave equations in an exterior domain in 2D, J. Differential Equations, 257 (2014), 2765-2800. ArXiv: 1204.3725v2.
doi: 10.1016/j.jde.2014.05.048. |
[15] |
K. Kubota, Existence of a global solutions to a semi-linear wave equation with initial data of non-compact support in low space dimensions, Hokkaido Math. J., 22 (1993), 123-180.
doi: 10.14492/hokmj/1381413170. |
[16] |
J. Metcalfe, Global existence for semilinear wave equations exterior to nontrapping obstacles, Houston J. Math., 30 (2004), 259-281. |
[17] |
J. Metcalfe, M. Nakamura and C. D. Sogge, Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition, Japan. J. Math. (N.S.), 31 (2005), 391-472. |
[18] |
J. Metcalfe and C. D. Sogge, Hyperbolic trapped rays and global existence of quasilinear wave equations, Invent. Math., 159 (2005), 75-117.
doi: 10.1007/s00222-004-0383-2. |
[19] |
Y. Shibata and Y. Tsutsumi, On a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain, Math. Z., 191 (1986), 165-199.
doi: 10.1007/BF01164023. |
[1] |
Moez Daoulatli. Energy decay rates for solutions of the wave equation with linear damping in exterior domain. Evolution Equations and Control Theory, 2016, 5 (1) : 37-59. doi: 10.3934/eect.2016.5.37 |
[2] |
Lucie Baudouin, Emmanuelle Crépeau, Julie Valein. Global Carleman estimate on a network for the wave equation and application to an inverse problem. Mathematical Control and Related Fields, 2011, 1 (3) : 307-330. doi: 10.3934/mcrf.2011.1.307 |
[3] |
Jun Zhou. Global existence and energy decay estimate of solutions for a class of nonlinear higher-order wave equation with general nonlinear dissipation and source term. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1175-1185. doi: 10.3934/dcdss.2017064 |
[4] |
Jeong Ja Bae, Mitsuhiro Nakao. Existence problem for the Kirchhoff type wave equation with a localized weakly nonlinear dissipation in exterior domains. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 731-743. doi: 10.3934/dcds.2004.11.731 |
[5] |
Linglong Du, Caixuan Ren. Pointwise wave behavior of the initial-boundary value problem for the nonlinear damped wave equation in $\mathbb{R}_{+}^{n} $. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3265-3280. doi: 10.3934/dcdsb.2018319 |
[6] |
Neal Bez, Chris Jeavons. A sharp Sobolev-Strichartz estimate for the wave equation. Electronic Research Announcements, 2015, 22: 46-54. doi: 10.3934/era.2015.22.46 |
[7] |
Seiji Ukai, Tong Yang, Huijiang Zhao. Exterior Problem of Boltzmann Equation with Temperature Difference. Communications on Pure and Applied Analysis, 2009, 8 (1) : 473-491. doi: 10.3934/cpaa.2009.8.473 |
[8] |
Yongqin Liu, Weike Wang. The pointwise estimates of solutions for dissipative wave equation in multi-dimensions. Discrete and Continuous Dynamical Systems, 2008, 20 (4) : 1013-1028. doi: 10.3934/dcds.2008.20.1013 |
[9] |
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 |
[10] |
Boris P. Belinskiy, Peter Caithamer. Energy estimate for the wave equation driven by a fractional Gaussian noise. Conference Publications, 2007, 2007 (Special) : 92-101. doi: 10.3934/proc.2007.2007.92 |
[11] |
Li-Ming Yeh. Pointwise estimate for elliptic equations in periodic perforated domains. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1961-1986. doi: 10.3934/cpaa.2015.14.1961 |
[12] |
Belkacem Said-Houari, Salim A. Messaoudi. General decay estimates for a Cauchy viscoelastic wave problem. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1541-1551. doi: 10.3934/cpaa.2014.13.1541 |
[13] |
Stéphane Gerbi, Belkacem Said-Houari. Exponential decay for solutions to semilinear damped wave equation. Discrete and Continuous Dynamical Systems - S, 2012, 5 (3) : 559-566. doi: 10.3934/dcdss.2012.5.559 |
[14] |
Rachid Assel, Mohamed Ghazel. Energy decay for the damped wave equation on an unbounded network. Evolution Equations and Control Theory, 2018, 7 (3) : 335-351. doi: 10.3934/eect.2018017 |
[15] |
Shumin Li, Masahiro Yamamoto, Bernadette Miara. A Carleman estimate for the linear shallow shell equation and an inverse source problem. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 367-380. doi: 10.3934/dcds.2009.23.367 |
[16] |
Soumen Senapati, Manmohan Vashisth. Stability estimate for a partial data inverse problem for the convection-diffusion equation. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021060 |
[17] |
Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557 |
[18] |
Hongjie Dong, Dapeng Du. Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1095-1101. doi: 10.3934/dcds.2008.21.1095 |
[19] |
Xue Yang, Xinglong Wu. Wave breaking and persistent decay of solution to a shallow water wave equation. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2149-2165. doi: 10.3934/dcdss.2016089 |
[20] |
Wenxiong Chen, Congming Li. A priori estimate for the Nirenberg problem. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 225-233. doi: 10.3934/dcdss.2008.1.225 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]