zbMATH — the first resource for mathematics

A new numerical model for propagation of tsunami waves. (English) Zbl 1140.35529
Summary: A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model.
35L70 Second-order nonlinear hyperbolic equations
47J30 Variational methods involving nonlinear operators
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74J15 Surface waves in solid mechanics
35R35 Free boundary problems for PDEs
Full Text: Link EuDML
[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 · Zbl 1059.35103 · doi:10.1088/0951-7715/17/3/010
[2] Kikuchi N.: An approach to the construction of Morse flows for variational functionals. Nematics - Mathematical and Physical Aspects (J. M. Coron, J. M. Ghidaglia, and F. Hélein, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 332 (1991), Kluwer Academic Publishers, Dodrecht - Boston - London, pp. 195-198 · 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 · 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 · Zbl 0892.65037 · doi:10.1016/S0362-546X(97)00397-0
[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 · 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 · Zbl 1122.35160
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.