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Asymptotic profiles for a strongly damped plate equation with lower order perturbation
1. | Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan, Japan |
References:
[1] |
R. C. Charão, C. R. daLuz and R. Ikehata, New decay rates for a problem of plate dynamics with fractional damping, J. Hyperbolic Diff. Eqns, 10 (2013), 1-13.
doi: 10.1142/S0219891613500203. |
[2] |
M. D'Abbicco and M. R. Ebert, Diffusion phenomena for the wave equation with structural damping in the $L^p$-$L^q$ framework, J. Diff. Eqns, 256 (2014), 2307-2336.
doi: 10.1016/j.jde.2014.01.002. |
[3] |
M. D'Abbicco and M. Reissig, Semi-linear structural damped waves, Math. Meth. Appl. Sci., 32 (2014), 1570-1592. |
[4] |
L. C. Evans, Partial Differential Equations, Berkeley Mathematics Lecture Noes Vol. 3a, 1994. |
[5] |
D. Hoff and K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J., 44 (1995), 603-676.
doi: 10.1512/iumj.1995.44.2003. |
[6] |
R. Ikehata, New decay estimates for linear damped wave equations and its application to nonlinear problem, Math. Meth. Appl. Sci., 27 (2004), 865-889.
doi: 10.1002/mma.476. |
[7] |
R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Diff. Eqns, 257 (2014), 2159-2177.
doi: 10.1016/j.jde.2014.05.031. |
[8] |
R. Ikehata and M. Natsume, Energy decay estimates for wave equations with a fractional damping, Diff. Int. Eqns, 25 (2012), 939-956. |
[9] |
R. Ikehata, G. Todorova and B. Yordanov, Wave equations with strong damping in Hilbert spaces, J. Diff. Eqns, 254 (2013), 3352-3368.
doi: 10.1016/j.jde.2013.01.023. |
[10] |
G. Karch, Selfsimilar profiles in large time asymptotics of solutions to damped wave equations, Studia Math., 143 (2000), 175-197. |
[11] |
X. Lu and M. Reissig, Rates of decay for structural damped models with decreasing in time coefficients, Int. J. Dyn. Syst. Differ. Equ., 2 (2009), 21-55.
doi: 10.1504/IJDSDE.2009.028034. |
[12] |
C. R. daLuz, R. Ikehata and R. C. Charão, Asymptotic behavior for abstract evolution differential equations of second order, J. Diff. Eqns, in press. |
[13] |
S. Mizohata, The Theory of Partial Differential Equations, Cambridge University Press, Cambridge, 1973. |
[14] |
G. Ponce, Global existence of small solutions to a class of nonlinear evolution equations, Nonlinear Anal., 9 (1985), 399-418.
doi: 10.1016/0362-546X(85)90001-X. |
[15] |
Y. Shibata, On the rate of decay of solutions to linear viscoelastic equation, Math. Meth. Appl. Sci., 23 (2000), 203-226.
doi: 10.1002/(SICI)1099-1476(200002)23:3<203::AID-MMA111>3.0.CO;2-M. |
[16] |
M. A. J. Silva and T. F. Ma, On a viscoelastic plate equation with history setting and perturbation of $p$-Laplacian type, IMA J. Appl. Math., 78 (2013), 1130-1146.
doi: 10.1093/imamat/hxs011. |
[17] |
H. Takeda and S. Yoshikawa, On the initial value problem of the semilinear beam equation with weak damping II, Asymptotic profiles, J. Diff. Eqns, 253 (2012), 3061-3080.
doi: 10.1016/j.jde.2012.07.014. |
[18] |
T. Umeda, S. Kawashima and Y. Shizuta, On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math., 1 (1984), 435-457.
doi: 10.1007/BF03167068. |
show all references
References:
[1] |
R. C. Charão, C. R. daLuz and R. Ikehata, New decay rates for a problem of plate dynamics with fractional damping, J. Hyperbolic Diff. Eqns, 10 (2013), 1-13.
doi: 10.1142/S0219891613500203. |
[2] |
M. D'Abbicco and M. R. Ebert, Diffusion phenomena for the wave equation with structural damping in the $L^p$-$L^q$ framework, J. Diff. Eqns, 256 (2014), 2307-2336.
doi: 10.1016/j.jde.2014.01.002. |
[3] |
M. D'Abbicco and M. Reissig, Semi-linear structural damped waves, Math. Meth. Appl. Sci., 32 (2014), 1570-1592. |
[4] |
L. C. Evans, Partial Differential Equations, Berkeley Mathematics Lecture Noes Vol. 3a, 1994. |
[5] |
D. Hoff and K. Zumbrun, Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow, Indiana Univ. Math. J., 44 (1995), 603-676.
doi: 10.1512/iumj.1995.44.2003. |
[6] |
R. Ikehata, New decay estimates for linear damped wave equations and its application to nonlinear problem, Math. Meth. Appl. Sci., 27 (2004), 865-889.
doi: 10.1002/mma.476. |
[7] |
R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Diff. Eqns, 257 (2014), 2159-2177.
doi: 10.1016/j.jde.2014.05.031. |
[8] |
R. Ikehata and M. Natsume, Energy decay estimates for wave equations with a fractional damping, Diff. Int. Eqns, 25 (2012), 939-956. |
[9] |
R. Ikehata, G. Todorova and B. Yordanov, Wave equations with strong damping in Hilbert spaces, J. Diff. Eqns, 254 (2013), 3352-3368.
doi: 10.1016/j.jde.2013.01.023. |
[10] |
G. Karch, Selfsimilar profiles in large time asymptotics of solutions to damped wave equations, Studia Math., 143 (2000), 175-197. |
[11] |
X. Lu and M. Reissig, Rates of decay for structural damped models with decreasing in time coefficients, Int. J. Dyn. Syst. Differ. Equ., 2 (2009), 21-55.
doi: 10.1504/IJDSDE.2009.028034. |
[12] |
C. R. daLuz, R. Ikehata and R. C. Charão, Asymptotic behavior for abstract evolution differential equations of second order, J. Diff. Eqns, in press. |
[13] |
S. Mizohata, The Theory of Partial Differential Equations, Cambridge University Press, Cambridge, 1973. |
[14] |
G. Ponce, Global existence of small solutions to a class of nonlinear evolution equations, Nonlinear Anal., 9 (1985), 399-418.
doi: 10.1016/0362-546X(85)90001-X. |
[15] |
Y. Shibata, On the rate of decay of solutions to linear viscoelastic equation, Math. Meth. Appl. Sci., 23 (2000), 203-226.
doi: 10.1002/(SICI)1099-1476(200002)23:3<203::AID-MMA111>3.0.CO;2-M. |
[16] |
M. A. J. Silva and T. F. Ma, On a viscoelastic plate equation with history setting and perturbation of $p$-Laplacian type, IMA J. Appl. Math., 78 (2013), 1130-1146.
doi: 10.1093/imamat/hxs011. |
[17] |
H. Takeda and S. Yoshikawa, On the initial value problem of the semilinear beam equation with weak damping II, Asymptotic profiles, J. Diff. Eqns, 253 (2012), 3061-3080.
doi: 10.1016/j.jde.2012.07.014. |
[18] |
T. Umeda, S. Kawashima and Y. Shizuta, On the decay of solutions to the linearized equations of electro-magneto-fluid dynamics, Japan J. Appl. Math., 1 (1984), 435-457.
doi: 10.1007/BF03167068. |
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