A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis
DOI10.1088/1361-6544/ac3c29zbMath1481.35331arXiv2008.10754OpenAlexW3081438060MaRDI QIDQ5019954
Samer Israwi, Henrik Kalisch, Theodoros Katsaounis, Dimitrios Mitsotakis
Publication date: 11 January 2022
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.10754
initial-boundary value problemsolitary wavesregularized shallow water equationsGalerkin/finite element methodBBM-BBM systemslip-wall boundary conditions
Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) A priori estimates in context of PDEs (35B45) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Soliton solutions (35C08)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The Cauchy problem on large time for surface waves Boussinesq systems
- Boussinesq systems of Bona-Smith type on plane domains: theory and numerical analysis
- Existence of solutions for a Boussinesq system on the half line and on a finite interval
- Practical use of variational principles for modeling water waves
- Mechanical balance laws for Boussinesq models of surface water waves
- Boussinesq-Peregrine water wave models and their numerical approximation
- Multiplication in Sobolev spaces, revisited
- Numerical solution of KdV-KdV systems of Boussinesq equations. I: The numerical scheme and generalized solitary waves
- Numerical solution of Boussinesq systems of the Bona-Smith family
- On initial-boundary value problems for a Boussinesq system of BBM-BBM type in a plane domain
- Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems
- Functional analysis, Sobolev spaces and partial differential equations
- The numerical modelling of long wave propagation in the framework of nonlinear dispersion models
- Boundary value problems for Boussinesq type systems
- Equations for bi-directional waves over an uneven bottom
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
- A Boussinesq system for two-way propagation of nonlinear dispersive waves
- Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
- Long wave approximations for water waves
- Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves
- On the influence of wave reflection on shoaling and breaking solitary Waves
- On some Boussinesq systems in two space dimensions: theory and numerical analysis
- Numerical solution of Boussinesq systems of KdV–KdV type: II. Evolution of radiating solitary waves
- Finite Element Methods for Navier-Stokes Equations
- A model for the two-way propagation of water waves in a channel
- Optimal L ∞ Estimates for the Finite Element Method on Irregular Meshes
- A finite element method for the one-dimensional extended Boussinesq equations
- Finite Volume Methods for Hyperbolic Problems
- Well-posedness of the Green–Naghdi and Boussinesq–Peregrine systems
- Finite Element Methods for Maxwell's Equations
- A Conservative Fully Discrete Numerical Method for the Regularized Shallow Water Wave Equations
- Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models
- Derivation of asymptotic two-dimensional time-dependent equations for surface water wave propagation
- Galerkin Finite Element Methods for Parabolic Problems
- Long waves on a beach
- Variational principles in continuum mechanics
- Model equations for long waves in nonlinear dispersive systems
