Asymptotics near the shore for 2D shallow water over sloping planar bottom

被引：0

作者：

Minenkov, Dmitrii S. ^{[1
]}

机构：

[1] Russian Acad Sci IPMech RAS, Ishlinsky Inst Problems Mech, Moscow, Russia

来源：

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE DAYS ON DIFFRACTION (DD) 2017 | 2017年

基金：

俄罗斯科学基金会;

关键词：

EQUATIONS; WAVE;

D O I：

暂无

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

A two-dimensional nonlinear run-up problem is studied for the special case of planar bottom. For two-dimensional shallow water equations, the Cauchy problem is considered. For initial data the wave generated by localized source is considered when it comes close to the shoreline. Asymptotics are constructed using perturbation theory and the Carrier-Greenspan transform for the coordinate x normal to the shoreline. Obtained formulas are explicit and can be easily computed using parametrically defined functions.

引用

页码：240 / 243

页数：4

共 13 条

[1]

[Anonymous], RUSSIAN J MATH PHYS

[2] WATER WAVES OF FINITE AMPLITUDE ON A SLOPING BEACH [J].

CARRIER, GF ;

GREENSPAN, HP .

JOURNAL OF FLUID MECHANICS, 1958, 4 (01) :97-109

[3] Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations [J].

Dobrokhotov, S. Yu. ;

Shafarevich, A. I. ;

Tirozzi, B. .

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2008, 15 (02) :192-221

[4] Description of tsunami propagation based on the Maslov canonical operator [J].

Dobrokhotov, S. Yu. ;

Sekerzh-Zenkovich, S. Ya. ;

Tirozzi, B. ;

Tudorovskii, T. Ya. .

DOKLADY MATHEMATICS, 2006, 74 (01) :592-596

[5] Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation [J].

Dobrokhotov, S. Yu. ;

Nazaikinskii, V. E. .

MATHEMATICAL NOTES, 2016, 100 (5-6) :695-713

[6]

[Доброхотов Сергей Юрьевич Dobrokhotov S.Yu.], 2009, [Фундаментальная и прикладная гидрофизика, Fundamental'naya i prikladnaya gidrofizika], V2, P15

[7]

[Доброхотов Сергей Юрьевич Dobrokhotov Sergei Yur'evich], 2010, [Алгебра и анализ, St. Petersburg Mathematical Journal, Algebra i analiz], V22, P67

[8]

[Доброхотов Сергей Юрьевич Dobrokhotov Sergei Yur'evich], 2010, [Успехи математических наук, Russian Mathematical Surveys, Uspekhi matematicheskikh nauk], V65, P185, DOI 10.4213/rm9342

[9]

Maslov V.P., 1981, Semi-Classical Approximations in Quantum Mechanics

[10] Asymptotics of the Solutions of the One-Dimensional Nonlinear System of Equations of Shallow Water with Degenerate Velocity [J].

Minenkov, D. S. .

MATHEMATICAL NOTES, 2012, 92 (5-6) :664-672

← 1 2 →