
Previous Article
Optimal design of an optical length of a rod with the given mass
 PROC Home
 This Issue

Next Article
Periodic solutions of BirkhoffLewis type for the nonlinear wave equation
Energy estimate for the wave equation driven by a fractional Gaussian noise
1.  Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 374032598, United States 
2.  Department of Mathematics & Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, IN 46408, United States 
[1] 
Rachid Assel, Mohamed Ghazel. Energy decay for the damped wave equation on an unbounded network. Evolution Equations & Control Theory, 2018, 7 (3) : 335351. doi: 10.3934/eect.2018017 
[2] 
Guolian Wang, Boling Guo. Stochastic Kortewegde Vries equation driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems  A, 2015, 35 (11) : 52555272. doi: 10.3934/dcds.2015.35.5255 
[3] 
Litan Yan, Xiuwei Yin. Optimal error estimates for fractional stochastic partial differential equation with fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2019, 24 (2) : 615635. doi: 10.3934/dcdsb.2018199 
[4] 
Yannick Privat, Emmanuel Trélat, Enrique Zuazua. Complexity and regularity of maximal energy domains for the wave equation with fixed initial data. Discrete & Continuous Dynamical Systems  A, 2015, 35 (12) : 61336153. doi: 10.3934/dcds.2015.35.6133 
[5] 
Moez Daoulatli. Energy decay rates for solutions of the wave equation with linear damping in exterior domain. Evolution Equations & Control Theory, 2016, 5 (1) : 3759. doi: 10.3934/eect.2016.5.37 
[6] 
Mohammad A. Rammaha, Daniel Toundykov, Zahava Wilstein. Global existence and decay of energy for a nonlinear wave equation with $p$Laplacian damping. Discrete & Continuous Dynamical Systems  A, 2012, 32 (12) : 43614390. doi: 10.3934/dcds.2012.32.4361 
[7] 
Joachim Krieger, Kenji Nakanishi, Wilhelm Schlag. Global dynamics of the nonradial energycritical wave equation above the ground state energy. Discrete & Continuous Dynamical Systems  A, 2013, 33 (6) : 24232450. doi: 10.3934/dcds.2013.33.2423 
[8] 
Brenton LeMesurier. Modeling thermal effects on nonlinear wave motion in biopolymers by a stochastic discrete nonlinear Schrödinger equation with phase damping. Discrete & Continuous Dynamical Systems  S, 2008, 1 (2) : 317327. doi: 10.3934/dcdss.2008.1.317 
[9] 
SunHo Choi. Weighted energy method and long wave short wave decomposition on the linearized compressible NavierStokes equation. Networks & Heterogeneous Media, 2013, 8 (2) : 465479. doi: 10.3934/nhm.2013.8.465 
[10] 
Miaomiao Niu, Zhongwei Tang. Least energy solutions for nonlinear Schrödinger equation involving the fractional Laplacian and critical growth. Discrete & Continuous Dynamical Systems  A, 2017, 37 (7) : 39633987. doi: 10.3934/dcds.2017168 
[11] 
Congming Peng, Dun Zhao. Global existence and blowup on the energy space for the inhomogeneous fractional nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  B, 2019, 24 (7) : 33353356. doi: 10.3934/dcdsb.2018323 
[12] 
Moez Daoulatli, Irena Lasiecka, Daniel Toundykov. Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions. Discrete & Continuous Dynamical Systems  S, 2009, 2 (1) : 6794. doi: 10.3934/dcdss.2009.2.67 
[13] 
Ferhat Mohamed, Hakem Ali. Energy decay of solutions for the wave equation with a timevarying delay term in the weakly nonlinear internal feedbacks. Discrete & Continuous Dynamical Systems  B, 2017, 22 (2) : 491506. doi: 10.3934/dcdsb.2017024 
[14] 
Yanbing Yang, Runzhang Xu. Nonlinear wave equation with both strongly and weakly damped terms: Supercritical initial energy finite time blow up. Communications on Pure & Applied Analysis, 2019, 18 (3) : 13511358. doi: 10.3934/cpaa.2019065 
[15] 
Gisèle Ruiz Goldstein, Jerome A. Goldstein, Fabiana Travessini De Cezaro. Equipartition of energy for nonautonomous wave equations. Discrete & Continuous Dynamical Systems  S, 2017, 10 (1) : 7585. doi: 10.3934/dcdss.2017004 
[16] 
Mohammad Akil, Ali Wehbe. Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions. Mathematical Control & Related Fields, 2019, 9 (1) : 97116. doi: 10.3934/mcrf.2019005 
[17] 
Jun Zhou. Global existence and energy decay estimate of solutions for a class of nonlinear higherorder wave equation with general nonlinear dissipation and source term. Discrete & Continuous Dynamical Systems  S, 2017, 10 (5) : 11751185. doi: 10.3934/dcdss.2017064 
[18] 
Mikko Kemppainen, Peter Sjögren, José Luis Torrea. Wave extension problem for the fractional Laplacian. Discrete & Continuous Dynamical Systems  A, 2015, 35 (10) : 49054929. doi: 10.3934/dcds.2015.35.4905 
[19] 
Annalisa Cesaroni, Matteo Novaga. Volume constrained minimizers of the fractional perimeter with a potential energy. Discrete & Continuous Dynamical Systems  S, 2017, 10 (4) : 715727. doi: 10.3934/dcdss.2017036 
[20] 
Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 11971212. doi: 10.3934/dcdsb.2014.19.1197 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]