-
Previous Article
Trajectory attractor for reaction-diffusion system with diffusion coefficient vanishing in time
- DCDS Home
- This Issue
-
Next Article
Numerical solution of a variational problem arising in stress analysis: The vector case
Decay of solutions to a water wave model with a nonlocal viscous dispersive term
1. | Department of Mathematics, Purdue University, West Lafayette, IN 47907 |
2. | LAMFA CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039 Amiens cedex |
3. | LAMFA CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039Amiens Cedex 1 |
4. | Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex |
$ u_t+u_x+\beta $uxxx$+\frac{\sqrt{\nu}}{\sqrt{\pi}}\int_0^t \frac{u_t(s)}{\sqrt{t-s}}ds+$uux$=\nu $uxx$. $
The wellposedness of the equation and the decay rate of solutions are investigated theoretically and numerically.
[1] |
Marcio Antonio Jorge da Silva, Vando Narciso. Long-time dynamics for a class of extensible beams with nonlocal nonlinear damping*. Evolution Equations and Control Theory, 2017, 6 (3) : 437-470. doi: 10.3934/eect.2017023 |
[2] |
H. A. Erbay, S. Erbay, A. Erkip. Long-time existence of solutions to nonlocal nonlinear bidirectional wave equations. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2877-2891. doi: 10.3934/dcds.2019119 |
[3] |
Igor Chueshov, Stanislav Kolbasin. Long-time dynamics in plate models with strong nonlinear damping. Communications on Pure and Applied Analysis, 2012, 11 (2) : 659-674. doi: 10.3934/cpaa.2012.11.659 |
[4] |
Vladimir Varlamov. Eigenfunction expansion method and the long-time asymptotics for the damped Boussinesq equation. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 675-702. doi: 10.3934/dcds.2001.7.675 |
[5] |
Mingming Chen, Xianguo Geng, Kedong Wang. Long-time asymptotics for the modified complex short pulse equation. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022060 |
[6] |
Vincent Duchêne, Samer Israwi, Raafat Talhouk. Shallow water asymptotic models for the propagation of internal waves. Discrete and Continuous Dynamical Systems - S, 2014, 7 (2) : 239-269. doi: 10.3934/dcdss.2014.7.239 |
[7] |
Robert McOwen, Peter Topalov. Asymptotics in shallow water waves. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3103-3131. doi: 10.3934/dcds.2015.35.3103 |
[8] |
Annalisa Iuorio, Stefano Melchionna. Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction. Discrete and Continuous Dynamical Systems, 2018, 38 (8) : 3765-3788. doi: 10.3934/dcds.2018163 |
[9] |
Chang Zhang, Fang Li, Jinqiao Duan. Long-time behavior of a class of nonlocal partial differential equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 749-763. doi: 10.3934/dcdsb.2018041 |
[10] |
Amjad Khan, Dmitry E. Pelinovsky. Long-time stability of small FPU solitary waves. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2065-2075. doi: 10.3934/dcds.2017088 |
[11] |
Min Chen, Olivier Goubet. Long-time asymptotic behavior of dissipative Boussinesq systems. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 509-528. doi: 10.3934/dcds.2007.17.509 |
[12] |
A. Kh. Khanmamedov. Long-time behaviour of doubly nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2009, 8 (4) : 1373-1400. doi: 10.3934/cpaa.2009.8.1373 |
[13] |
A. Kh. Khanmamedov. Long-time behaviour of wave equations with nonlinear interior damping. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1185-1198. doi: 10.3934/dcds.2008.21.1185 |
[14] |
Jiaohui Xu, Tomás Caraballo, José Valero. Asymptotic behavior of nonlocal partial differential equations with long time memory. Discrete and Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021140 |
[15] |
Jianping Wang, Mingxin Wang. Free boundary problems with nonlocal and local diffusions Ⅱ: Spreading-vanishing and long-time behavior. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4721-4736. doi: 10.3934/dcdsb.2020121 |
[16] |
Elena Kartashova. Nonlinear resonances of water waves. Discrete and Continuous Dynamical Systems - B, 2009, 12 (3) : 607-621. doi: 10.3934/dcdsb.2009.12.607 |
[17] |
Min Chen, Olivier Goubet. Long-time asymptotic behavior of two-dimensional dissipative Boussinesq systems. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 37-53. doi: 10.3934/dcdss.2009.2.37 |
[18] |
Xia Li. Long-time asymptotic solutions of convex hamilton-jacobi equations depending on unknown functions. Discrete and Continuous Dynamical Systems, 2017, 37 (10) : 5151-5162. doi: 10.3934/dcds.2017223 |
[19] |
Linghai Zhang. Long-time asymptotic behaviors of solutions of $N$-dimensional dissipative partial differential equations. Discrete and Continuous Dynamical Systems, 2002, 8 (4) : 1025-1042. doi: 10.3934/dcds.2002.8.1025 |
[20] |
Chaoying Li, Xiaojing Xu, Zhuan Ye. On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model. Discrete and Continuous Dynamical Systems, 2022, 42 (3) : 1535-1568. doi: 10.3934/dcds.2021163 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]