Full entry |
PDF
(0.7 MB)
Feedback

long waves; nonlinear hyperbolic equation; volume constraint; free boundary; variational method; discrete Morse semi-flow; FEM

References:

[1] Bona J. L., Chen M., Saut J.-C.: **Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media**. I: Derivation and linear theory. J. Nonlinear Sci. 12 (2002), 283–318 DOI 10.1007/s00332-002-0466-4 | MR 1915939 | Zbl 1059.35103

[2] Kikuchi N.: **An approach to the construction of Morse flows for variational functionals**. In: Nematics – Mathematical and Physical Aspects (J. M. Coron, J. M. Ghidaglia, and F. Hélein, eds.), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 332 (1991), Kluwer Academic Publishers, Dodrecht – Boston – London, pp. 195–198 MR 1178095 | Zbl 0850.76043

[3] Nagasawa T., Omata S.: **Discrete Morse semiflows of a functional with free boundary**. Adv. Math. Sci. Appl. 2 (1993), 147–187 MR 1239254 | Zbl 0795.35150

[4] Omata S.: **A numerical method based on the discrete Morse semiflow related to parabolic and hyperbolic equations**. Nonlinear Anal. 30 (1997), 2181–2187 DOI 10.1016/S0362-546X(97)00397-0 | MR 1490340

[5] Švadlenka K., Omata S.: **Construction of weak solution to hyperbolic problem with volume constraint**. Submitted to Nonlinear Anal

[6] Yamazaki T., Omata S., Švadlenka, K., Ohara K.: **Construction of approximate solution to a hyperbolic free boundary problem with volume constraint and its numerical computation**. Adv. Math. Sci. Appl. 16 (2006), 57–67 MR 2253225 | Zbl 1122.35159

[7] Yoshiuchi H., Omata S., Švadlenka, K., Ohara K.: **Numerical solution of film vibration with obstacle**. Adv. Math. Sci. Appl. 16 (2006), 33–43 MR 2253223 | Zbl 1122.35160