Kolmogorov's epsilon-entropy of the attractor of the strongly damped wave equation in locally uniform spaces
- Proceedings of Equadiff 14, Publisher: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing(Bratislava), page 69-78
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topSlavík, Jakub. "Kolmogorov's epsilon-entropy of the attractor of the strongly damped wave equation in locally uniform spaces." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 69-78. <http://eudml.org/doc/294924>.
@inProceedings{Slavík2017,
abstract = {We establish an upper bound on the Kolmogorov’s entropy of the locally compact attractor for strongly damped wave equation posed in locally uniform spaces in subcritical case using the method of trajectories.},
author = {Slavík, Jakub},
booktitle = {Proceedings of Equadiff 14},
keywords = {Strongly damped wave equation, unbounded domains, locally compact attractor, Kolmogorovs entropy.},
location = {Bratislava},
pages = {69-78},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {Kolmogorov's epsilon-entropy of the attractor of the strongly damped wave equation in locally uniform spaces},
url = {http://eudml.org/doc/294924},
year = {2017},
}
TY - CLSWK
AU - Slavík, Jakub
TI - Kolmogorov's epsilon-entropy of the attractor of the strongly damped wave equation in locally uniform spaces
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 69
EP - 78
AB - We establish an upper bound on the Kolmogorov’s entropy of the locally compact attractor for strongly damped wave equation posed in locally uniform spaces in subcritical case using the method of trajectories.
KW - Strongly damped wave equation, unbounded domains, locally compact attractor, Kolmogorovs entropy.
UR - http://eudml.org/doc/294924
ER -
References
top- Belleri, V., Pata, V., Attractors for semilinear strongly damped wave equations on , , Discrete Contin. Dynam. Systems, 7 (2001), pp. 719–735. MR1849655
- Carvalho, A. N., Cholewa, J. W., Attractors for strongly damped wave equations with critical nonlinearities, , Pacific J. Math., 207 (2002), pp. 287–310. MR1972247
- Cholewa, J. W., Dlotko, T., Strongly damped wave equation in uniform spaces, , Nonlinear Anal., 64 (2006), pp. 174–187. MR2183836
- Conti, M., Pata, V., Squassina, M., Strongly damped wave equations on with critical nonlinearities, , Commun. Appl. Anal., 9 (2005), pp. 161–176. MR2168756
- Plinio, F. Di, Pata, V., Zelik, S., On the strongly damped wave equation with memory, , Indiana Univ. Math. J., 57 (2008), pp. 757–780. MR2414334
- Ghidaglia, J.-M., Marzocchi, A., Longtime behaviour of strongly damped wave equations, global attractors and their dimension, , SIAM J. Math. Anal., 22 (1991), pp. 879–895. MR1112054
- Grasselli, M., Pražák, D., Schimperna, G., Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories, , J. Differential Equations, 249 (2010), pp. 2287–2315. MR2718659
- Kalantarov, V., Zelik, S., Finite-dimensional attractors for the quasi-linear strongly damped wave equation, , J. Differential Equations, 247 (2009), pp. 1120–1155. MR2531174
- Li, H., Zhou, S., Kolmogorov ε-entropy of attractor for a non-autonomous strongly damped wave equation, , Commun. Nonlinear Sci. Numer. Simul., 17 (2012), pp. 3579–3586. MR2913994
- Michálek, M., Pražák, D., HASH(0x2ff9058), Slavík, J., Semilinear damped wave equation in locally uniform spaces, , Commun. Pure Appl. Anal., 16 (2017), pp. 1673–1695. MR3661796
- Pata, V., Squassina, M., On the strongly damped wave equation, , Comm. Math. Phys., 253 (2005), pp. 511–533. MR2116726
- Pražák, D., On finite fractal dimension of the global attractor for the wave equation with nonlinear damping, , J. Dynam. Differential Equations, 14 (2002), pp. 763–776. MR1940102
- Roubíček, T., Nonlinear partial differential equations with applications, , Birkhäuser/Springer Basel AG, Basel, International Series of Numerical Mathematics 153 (2013). MR3014456
- Savostianov, A., Infinite energy solutions for critical wave equation with fractional damping in unbounded domains, , Nonlinear Anal., 136 (2016), pp. 136–167. MR3474408
- Yang, M., Sun, C., Dynamics of strongly damped wave equations in locally uniform spaces: attractors and asymptotic regularity, , Trans. Amer. Math. Soc., 361 (2009), pp. 1069–1101. MR2452835
- Yang, M., Sun, C., Exponential attractors for the strongly damped wave equations, , Nonlinear Anal. Real World Appl., 11 (2010), pp. 913–919. MR2571264
- Zelik, S. V., The attractor for a nonlinear hyperbolic equation in the unbounded domain, , Discrete Contin. Dynam. Systems, 7 (2001), pp. 593–641. MR1815770
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