scholarly journals Wave-breaking phenomena and global existence for the generalized Fornberg-Whitham equation

2021 ◽  
Vol 502 (1) ◽  
pp. 125247
Author(s):  
Kenta Itasaka
Keyword(s):  
Global Existence ◽  
Wave Breaking ◽  
Whitham Equation

scholarly journals Solution concepts, well-posedness, and wave breaking for the Fornberg–Whitham equation

2020 ◽  
Author(s):  
Günther Hörmann
Keyword(s):  
Cauchy Problem ◽  
Traveling Waves ◽  
Wave Breaking ◽  
Blow Up ◽  
Strong Solutions ◽  
Well Posedness ◽  
Solution Concepts ◽  
Nonlinear Operators ◽  
The Cauchy Problem ◽  
Whitham Equation

AbstractWe discuss concepts and review results about the Cauchy problem for the Fornberg–Whitham equation, which has also been called Burgers–Poisson equation in the literature. Our focus is on a comparison of various strong and weak solution concepts as well as on blow-up of strong solutions in the form of wave breaking. Along the way we add aspects regarding semiboundedness at blow-up, from semigroups of nonlinear operators to the Cauchy problem, and about continuous traveling waves as weak solutions.

scholarly journals The dynamic properties of solutions for a nonlinear shallow water equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yeqin Su ◽  
Shaoyong Lai ◽  
Sen Ming
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Shallow Water ◽  
Wave Breaking ◽  
Dynamic Properties ◽  
Shallow Water Equation ◽  
Propagation Speed ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
Infinite Propagation Speed

Abstract The local well-posedness for the Cauchy problem of a nonlinear shallow water equation is established. The wave-breaking mechanisms, global existence, and infinite propagation speed of solutions to the equation are derived under certain assumptions. In addition, the effects of coefficients λ, β, a, b, and index k in the equation are illustrated.

scholarly journals Publisher Correction to: On the stochastic Dullin–Gottwald–Holm equation: global existence and wave-breaking phenomena

2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Christian Rohde ◽  
Hao Tang
Keyword(s):  
Global Existence ◽  
Wave Breaking ◽  
Original Publication ◽  
Holm Equation

During the typesetting process, some misprints have been introduced in the original publication of the article.

scholarly journals Wave breaking for the Whitham equation with fractional dispersion

Nonlinearity ◽  
2014 ◽  
Vol 27 (12) ◽  
pp. 2937-2949 ◽  
Author(s):  
Vera Mikyoung Hur ◽  
Lizheng Tao
Keyword(s):  
Wave Breaking ◽  
Whitham Equation
Sign in / Sign up

Export Citation Format

Share Document