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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 568404, 12 pages
The Local Strong and Weak Solutions for a Generalized Pseudoparabolic Equation
Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, China
Received 7 February 2012; Accepted 21 March 2012
Academic Editor: Yonghong Wu
Copyright © 2012 Nan Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- P. L. Davis, “A quasilinear parabolic and a related third order problem,” Journal of Mathematical Analysis and Applications, vol. 40, pp. 327–335, 1972.
- B. D. Coleman and W. Noll, “An approximation theorem for functionals, with applications in continuum mechanics,” Archive for Rational Mechanics and Analysis, vol. 6, no. 1, pp. 355–370, 1960.
- R. E. Showalter and T. W. Ting, “Pseudoparabolic partial differential equations,” SIAM Journal on Mathematical Analysis, vol. 1, pp. 1–26, 1970.
- G. W. Chen and H. X. Xue, “Global existence of solution of Cauchy problem for nonlinear pseudo-parabolic equation,” Journal of Differential Equations, vol. 245, no. 10, pp. 2705–2722, 2008.
- P. G. Kevrekidis, I. G. Kevrekidis, A. R. Bishop, and E. S. Titi, “Continuum approach to discreteness,” Physical Review E, vol. 65, no. 4, Article ID 046613, 13 pages, 2002.
- J. L. Bona and L. Luo, “Asymptotic decomposition of nonlinear, dispersive wave equations with dissipation,” Physica D, vol. 152–153, pp. 363–383, 2001.
- J. Albert, “Dispersion of low-energy waves for the generalized Benjamin-Bona-Mahony equation,” Journal of Differential Equations, vol. 63, no. 1, pp. 117–134, 1986.
- T. Kato and G. Ponce, “Commutator estimates and the Euler and Navier-Stokes equations,” Communications on Pure and Applied Mathematics, vol. 41, no. 7, pp. 891–907, 1988.
- S. Y. Lai and Y. H. Wu, “The local well-posedness and existence of weak solutions for a generalized Camassa-Holm equation,” Journal of Differential Equations, vol. 248, no. 8, pp. 2038–2063, 2010.
- S. Y. Lai and Y. H. Wu, “Existence of weak solutions in lower order Sobolev space for a Camassa-Holm-type equation,” Journal of Physics A, vol. 43, no. 9, Article ID 095205, 13 pages, 2010.
- Y. A. Li and P. Olver, “Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation,” Journal of Differential Equations, vol. 162, no. 1, pp. 27–63, 2000.