Displaying similar documents to “New Approach to Shocks Generation for Conservation Laws. Example: Global Solution to Hopf Equation”

Shoaling of nonlinear steady waves: maximum height and angle of breaking

Franco, Sebastião Romero, Farina, Leandro

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A Fourier approximation method is used for modeling and simulation of fully nonlinear steady waves. The set of resulting nonlinear equations are solved by Newton's method. The shoaling of waves is simulated based on comparisons with experimental data. The wave heights and the angles of breaking are analysed until the limit of inadequacy of the numerical method. The results appear quite close to those criteria predicted by the theory of completely nonlinear surface waves and contribute...

Zero-Dissipation Limit for Nonlinear Waves

Jerry L. Bona, Jiahong Wu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Evolution equations featuring nonlinearity, dispersion and dissipation are considered here. For classes of such equations that include the Korteweg-de Vries-Burgers equation and the BBM-Burgers equation, the zero dissipation limit is studied. Uniform bounds independent of the dissipation coefficient are derived and zero dissipation limit results with optimal convergence rates are established.

A finite element method for extended KdV equations

Anna Karczewska, Piotr Rozmej, Maciej Szczeciński, Bartosz Boguniewicz (2016)

International Journal of Applied Mathematics and Computer Science

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The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic...

Continuous dependence and general decay of solutions for a wave equation with a nonlinear memory term

Doan Thi Nhu Quynh, Nguyen Huu Nhan, Le Thi Phuong Ngoc, Nguyen Thanh Long (2023)

Applications of Mathematics

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We study existence, uniqueness, continuous dependence, general decay of solutions of an initial boundary value problem for a viscoelastic wave equation with strong damping and nonlinear memory term. At first, we state and prove a theorem involving local existence and uniqueness of a weak solution. Next, we establish a sufficient condition to get an estimate of the continuous dependence of the solution with respect to the kernel function and the nonlinear terms. Finally, under suitable...