Paper Titles

The Application of Multi-Hypothesis Targets Algorithm in Track Association
p.736

Method of Suppressing Noise AM Jamming with EMD for Combined Modulation Radio Ranging System
p.739

Studies to Determine the Wind Profile Radar SNR Threshold Method
p.744

Study of Flexible Waterproof Layer Thickness Measuring Based on B-Mode Ultrasound Image
p.749

The Solutions for a Kind of Engineering Equation
p.753

A Method of Indoor Localization Based on BLE4.0 Protocol of Using Beacons
p.765

An Inclusion Measure between Fuzzy Sets
p.769

Manufacturing Cloud Service Model Based on Adaptive Mechanism
p.773

A Load-Balanced Coding-Aware Multicast Routing in Cognitive Wireless Mesh Networks
p.777

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 740The Solutions for a Kind of Engineering Equation

The Solutions for a Kind of Engineering Equation

Article Preview

Abstract:

A class of shallow water waves equations are studied in this paper. Using Kato's existence theorem, we mainly study the initial and bounded value problem for the quasi-linear evolution equations. Meanwhile, we prove the existence of local and global existence of solutions to the equations.

You might also be interested in these eBooks

Mechanical, Information and Industrial Engineering

Info:

Periodical:

Applied Mechanics and Materials (Volume 740)

Pages:

753-762

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.740.753

Citation:

Cite this paper

Online since:

March 2015

Authors:

You Liang Fu*, Da Hang Zhang

Keywords:

Kato's Existence Theorem, Nonlinear, Shallow Water Waves Equations, Solutions

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2015 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] D. D. Holm and M. F. Staley: Physics Letters A, 308 (2003), 437-444.

[2] H. R. Dullin, G. A. Gottwald, and D. D. Holm: Physical Review Letters , 87 (2001), 4501-4504.

[3] L. Tian, G. Gui, and Y. Liu: Journal of Differential Equations, 245 (2008), 1838-1852.

[4] A. Degasperis and M. Procesi: Symmetry and Perturbation Theory (Rome, 1998), A. Degasperis and G. Gaeta, Eds., World Scientific, River Edge, NJ, USA, 1999 (1999), 23-37.

[5] R. Camassa and D. D. Holm: Physical Review Letters, 71 (1993), 1661-1664.

[6] S. Zhou and C. Mu: Journal of Differential Equations, 256 (2014), 1793-1816.

[7] A. Degasperis, D. D. Kholm, and A. N. I. Khon: Teoreticheskaya i Matematicheskaya Fizika, 133 (2002), 170-183.

[8] B. Fuchssteiner and A. S. Fokas: Physica D: Nonlinear Phenomena, 4 (1981), 47-66.

[9] B. Fuchssteiner: Physica D: Nonlinear Phenomena, 95 (1996), 229-243.

[10] A. Constantin: Proceedings of the Royal Society A, 457 (2001), 953-970.

[11] L. Yong and H. Yan: Mathematical Problems in Engineering, 2014 (2014).

[12] J. Lenells: Journal of Differential Equations, 217 (2005), 393-430.

[13] A. Constantin and W. A. Strauss: Journal of Nonlinear Science, 12 (2002), 415-422.

[14] A. Constantin and J. Escher: Communications on Pure and Applied Mathematics, 51 (1998), 475-504.

[15] A. Constantin: Annales de l'Institut Fourier, 50 (2000), 321-362.

[16] X. Liu and J. Liu: Nonlinear Analysis, 107 (2014), 1-17.

[17] G. Rodríguez-Blanco: Nonlinear Analysis: Theory, Methods & App., 46 (2001), 309-327.

[18] H. Dai, K. H. Kwek, H. Gao, and C. Qu: Frontiers of Mathematics in China, 1 (2006), 144-159.

[19] A. Constantin and J. Escher: Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV, 26 (1998), 303-328.

DOI: 10.2422/2036-2145.201706_022

[20] Y. A. Li and P. J. Olver: Journal of Differential Equations, 162 (2000), 27-63.

[21] N. Duruk Mutlubas: Nonlinear Analysis, 97 (2014), 145-154.

[22] A. Bressan and A. Constantin: Archive for Rational Mechanics and Analysis, 183 (2007), 215-239.

[23] Z. Xin and P. Zhang: Communications on Pure and Applied Mathematics, 53 (2000), 1411-1433.

[24] A. Constantin and W. A. Strauss: Communications on Pure and Applied Mathematics, 53 (2000), 603-610.

[25] H. R. Dullin, G. A. Gottwald, and D. D. Holm: Fluid Dynamics Research, 33 (2003), 73-95.

[26] Y. Tang and P. Su: Mathematical Analysis, 2012 (2012).

[27] D. D. Holm and M. E. Staley: SIAM Journal on Applied Dynamical Systems, 2 (2003), 323-380.

[28] Y. Matsuno: Inverse Problems, 21 (2005), 1553-1570.

[29] H. Lundmark and Journal Szmigielski: Inverse Problems, 19 (2003), 1241-1245.

[30] Z. Yin: Illinois Journal of Mathematics, 47 (2003), 649-666.

[31] A. M. Wazwaz: Applied Mathematics and Computation, 217 (2011), 8840-8845.

[32] Z. Yin: Journal of Mathematical Analysis and Applications, 283 (2003), 129-139.

[33] Z. Yin: Indiana University Mathematics Journal, 53 (2004), 1189-1209.

[34] Z. Yin: Journal of Functional Analysis, 212 (2004), 182-194.

[35] Y. Liu and Z. Yin: Communications in Mathematical Physics, 267 (2006), 801-820.

[36] W. Zhang and J. Zhou: Advances in Mathematical Physics, 2013 (2013).

[37] J. Escher, Y. Liu and Z. Yin: Journal of Functional Analysis, 241 (2006), 457-485.

[38] J. Escher, Y. Liu and Z. Yin: Indiana University Mathematics Journal, 56 (2007), 87-117.

[39] G. M. Coclite and K. H. Karlsen: Journal of Functional Analysis, 233 (2006), 60-91.

[40] L. Yang, B. Guo: Mathematical Theory and Applications (in Chinese), 2003 (2003), 1-10.

[41] T. Kato: Spectral Theory and Differential Equations, 448 (1975), 25-70.