scholarly journals Hydroelastic interaction between water waves and an array of circular floating porous elastic plates

2020 ◽  
Vol 900 ◽  
Author(s):  
Siming Zheng ◽  
Michael H. Meylan ◽  
Guixun Zhu ◽  
Deborah Greaves ◽  
Gregorio Iglesias
Keyword(s):  
Water Waves ◽  
Elastic Plates ◽  
Image Position ◽  
Hydroelastic Interaction

Abstract

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

scholarly journals Decay estimates for solutions of nonlocal semilinear equations

2015 ◽  
Vol 218 ◽  
pp. 175-198 ◽  
Author(s):  
Marco Cappiello ◽  
Todor Gramchev ◽  
Luigi Rodino
Keyword(s):  
Water Waves ◽  
Fourier Multiplier ◽  
Sobolev Type ◽  
Decay Estimates ◽  
Shallow Water Waves ◽  
Algebraic Decay ◽  
Semilinear Equations ◽  
Nonlocal Equations ◽  
Image Position ◽  
Strong Contrast

AbstractWe investigate the decay for |x|→∞ of weak Sobolev-type solutions of semilinear nonlocal equations Pu = F(u). We consider the case when P = p(D) is an elliptic Fourier multiplier with polyhomogeneous symbol p(ξ), and we derive algebraic decay estimates in terms of weighted Sobolev norms. Our basic example is the celebrated Benjamin–Ono equation for internal solitary waves of deep stratified fluids. Their profile presents algebraic decay, in strong contrast with the exponential decay for KdV shallow water waves.

On the existence theory for irrotational water waves

1978 ◽  
Vol 83 (1) ◽  
pp. 137-157 ◽  
Author(s):  
G. Keady ◽  
J. Norbury
Keyword(s):  
Water Waves ◽  
Volume Flow Rate ◽  
Ideal Liquid ◽  
Flow Speed ◽  
Existence Theory ◽  
Wave Solutions ◽  
Maximum Angle ◽  
Steady Plane ◽  
Image Position ◽  
The Waves

AbstractThis paper concerns steady plane periodic waves on the surface of an ideal liquid flowing above a horizontal bottom. The flow is irrotational. The volume flow rate is denoted by Q, the velocity potential by ø, the period in ø of the waves by 2L, and the maximum angle of inclination between the tangent to the surface and the horizontal by θm.Krasovskii (12) established that, at each fixed Q and L, there exist wave solutions for each value of θm strictly between zero and ⅙π. We establish that, at each fixed Q and L, there exist wave solutions for each value of qc strictly between c and zero. Here qc is the flow speed at the crest, andwhere g is the acceleration due to gravity. Krasovskii's set of solutions is included in the set that we obtain.

A model for the two-way propagation of water waves in a channel

1976 ◽  
Vol 79 (1) ◽  
pp. 167-182 ◽  
Author(s):  
Jerry L. Bona ◽  
Ronald Smith
Keyword(s):  
Water Waves ◽  
Open Channel ◽  
Boussinesq Equations ◽  
Coupled System ◽  
Finite Amplitude ◽  
Regularity Of Solutions ◽  
Initial Value ◽  
One Dimensional ◽  
Image Position ◽  
Continuous Dependence Of Solutions

Global existence, uniqueness and regularity of solutions and continuous dependence of solutions on varied initial data are established for the initial-value problem for the coupled system of equationsThis system has the same formal justification as a model for the two-way propagation of (one-dimensional) long waves of small but finite amplitude in an open channel of water of constant depth as other versions of the Boussinesq equations. A feature of the analysis is that bounds on the wave amplitude η are obtained which are valid for all time.

A mathematical model for long waves generated by wavemakers in non-linear dispersive systems

1973 ◽  
Vol 73 (2) ◽  
pp. 391-405 ◽  
Author(s):  
J. L. Bona ◽  
P. J. Bryant
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Water Waves ◽  
Open Channel ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Finite Amplitude ◽  
Mathematical Properties ◽  
Image Position ◽  
Initial Boundary Value

An initial-boundary-value problem for the equationis considered for x, t ≥ 0. This system is a model for long water waves of small but finite amplitude, generated in a uniform open channel by a wavemaker at one end. It is shown that, in contrast to an alternative, more familiar model using the Korteweg–deVries equation, the solution of (a) has good mathematical properties: in particular, the problem is well set in Hadamard's classical sense that solutions corresponding to given initial data exist, are unique, and depend continuously on the specified data.

Solitary wave solutions for a model of the two-way propagation of water waves in a channel

1981 ◽  
Vol 90 (2) ◽  
pp. 343-360 ◽  
Author(s):  
J. F. Toland
Keyword(s):  
Initial Data ◽  
Water Waves ◽  
Coupled System ◽  
Finite Amplitude ◽  
Solitary Wave Solutions ◽  
Flat Bottom ◽  
One Dimensional ◽  
Image Position ◽  
System 1 ◽  
Relevant Class

Bona and Smith (6) have suggested that the coupled system of equationshas the same formal justification as other Boussinesq-type models for the two-way propagation of one-dimensional water waves of small but finite amplitude in a channel with a flat bottom. The variables u and η represent the velocity and elevation of the free surface, respectively. Using the energy invariantthey show that for a restricted, but nevertheless physically relevant, class of initial data, the system (1·1) has solutions which exist for all time, and that in such circumstances the wave height is bounded solely in terms of the initial data.

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