
AIMS Mathematics, 2017, 2(1): 115. doi: 10.3934/Math.2017.1.1.
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Remarks on an elliptic problem arising in weighted energy estimates for wave equations with spacedependent damping term in an exterior domain
1 Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Nodashi, Chibaken 2788510, Japan
2 Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 4648602 Japan
Received: , Accepted: , Published:
Keywords: Damped wave equation; elliptic problem; exterior domain; weighted energy estimates; diffusion phenomena
Citation: Motohiro Sobajima, Yuta Wakasugi. Remarks on an elliptic problem arising in weighted energy estimates for wave equations with spacedependent damping term in an exterior domain. AIMS Mathematics, 2017, 2(1): 115. doi: 10.3934/Math.2017.1.1
References:
 1. M. Ikawa, Mixed problems for hyperbolic equations of second order, J. Math. Soc. Japan, 20 (1968), 580608.
 2. M. Ikawa, M. Ikawa, Hyperbolic partial diﬀerential equations and wave phenomena, American Mathematical Society, Providence, RI, 2000.
 3. R. Ikehata, Some remarks on the wave equation with potential type damping coeﬃcients, Int. J. Pure Appl. Math., 21 (2005), 1924.
 4. A. Matsumura, On the asymptotic behavior of solutions of semilinear wave equations, Publ. Res. Inst. Math. Sci., 12 (1976), 169189.
 5. A. Matsumura, Energy decay of solutions of dissipative wave equations, Proc. Japan Acad., Ser. A, 53 (1977), 232236.
 6. K. Mochizuki, Scattering theory for wave equations with dissipative terms, Publ. Res. Inst. Math. Sci., 12 (1976), 383390.
 7. K. Nishihara, L^{p}L^{q }estimates of solutions to the damped wave equation in 3dimensional space and their application, Math. Z., 244 (2003), 631649.
 8. P. Radu,G.Todorova,andB.Yordanov,Higher order energy decay rates for damped wave equations with variable coeﬃcients, Discrete Contin. Dyn. Syst. Ser. S, 2(2009), 609629.
 9. P. Radu, G.Todorova, and B.Yordanov,Decay estimates for wave equations with variable coeﬃcients,Trans. Amer. Math. Soc., 362 (2010), 22792299.
 10. M. Sobajima andY.Wakasugi, Diﬀusion phenomena for the wave equation with spacedependent damping in an exterior domain, J. Diﬀerential Equations, 261 (2016), 56905718.
 11. G.Todorova, andB.Yordanov, Critical exponent for a nonlinear wave equation with damping, J. Diﬀerential Equations, 174 (2001), 464489.
 12. G.Todorova, andB.Yordanov, Weighted L^{2}estimates for dissipative wave equations with variable coeﬃcients, J. Diﬀerential Equations, 246 (2009), 44974518
 13.Y.Wakasugi, On diﬀusion phenomena for the linear wave equation with spacedependent damping, J. Hyp. Diﬀ. Eq., 11 (2014), 795819.
This article has been cited by:
 1. Motohiro Sobajima, Yuta Wakasugi, Weighted energy estimates for wave equation with spacedependent damping term for slowly decaying initial data, Communications in Contemporary Mathematics, 2018, 10.1142/S0219199718500359
 2. Kenji Nishihara, Motohiro Sobajima, Yuta Wakasugi, Critical exponent for the semilinear wave equations with a damping increasing in the far field, Nonlinear Differential Equations and Applications NoDEA, 2018, 25, 6, 10.1007/s0003001805462
Reader Comments
Copyright Info: 2017, Motohiro Sobajima, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)
Associated material
Metrics
Other articles by authors
Related pages
Tools
your name: * your email: *