Continuous dependence on data under the Lipschitz metric for the rotation-Camassa-Holm equation

2020 ◽  
Vol 41 (1) ◽  
pp. 1-18
Author(s):  
Xinyu Tu ◽  
Chunlai Mu ◽  
Shuyan Qiu
Keyword(s):  
Continuous Dependence ◽  
Holm Equation ◽  
Lipschitz Metric ◽  
Continuous Dependence On Data

scholarly journals Anti-periodic traveling wave solutions to a class of higher-order Kadomtsev-Petviashvili-Burgers equations

1994 ◽  
Vol 7 (1) ◽  
pp. 1-12
Author(s):  
Sergiu Aizicovici ◽  
Yun Gao ◽  
Shih-Liang Wen
Keyword(s):  
Traveling Wave ◽  
Continuous Dependence ◽  
Traveling Wave Solutions ◽  
Higher Order ◽  
Two Dimensional ◽  
Burgers Equations ◽  
Wave Solutions ◽  
Periodic Traveling Wave ◽  
Continuous Dependence On Data

We discuss the existence, uniqueness, and continuous dependence on data, of anti-periodic traveling wave solutions to higher order two-dimensional equations of Korteweg-deVries type.

scholarly journals A LIPSCHITZ METRIC FOR THE CAMASSA–HOLM EQUATION

2020 ◽  
Vol 8 ◽  
Author(s):  
JOSÉ A. CARRILLO ◽  
KATRIN GRUNERT ◽  
HELGE HOLDEN
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Wasserstein Metric ◽  
Holm Equation ◽  
The Cauchy Problem ◽  
Lipschitz Metric

We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of the solution itself. In order to obtain uniqueness, one is required to augment the equation itself by a measure that represents the associated energy, and the breakdown of the solution is associated with a complicated interplay where the measure becomes singular. The main result in this paper is the construction of a Lipschitz metric that compares two solutions of the CH equation with the respective initial data. The Lipschitz metric is based on the use of the Wasserstein metric.

scholarly journals Lipschitz metric for the periodic Camassa–Holm equation

2011 ◽  
Vol 250 (3) ◽  
pp. 1460-1492 ◽  
Author(s):  
Katrin Grunert ◽  
Helge Holden ◽  
Xavier Raynaud
Keyword(s):  
Holm Equation ◽  
Lipschitz Metric

scholarly journals Lipschitz metric for the Camassa--Holm equation on the line

2013 ◽  
Vol 33 (7) ◽  
pp. 2809-2827 ◽  
Author(s):  
Katrin Grunert ◽  
◽  
Helge Holden ◽  
Xavier Raynaud ◽  
Keyword(s):  
Holm Equation ◽  
Lipschitz Metric

Continuous Dependence on Data for Solutions of Fractional Extended Fisher–Kolmogorov Equation

2018 ◽  
Vol 19 (7-8) ◽  
pp. 735-739
Author(s):  
Pengyu Chen ◽  
Zhen Xin ◽  
Jiahui An
Keyword(s):  
Boundary Value Problem ◽  
General Class ◽  
Continuous Dependence ◽  
Mild Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Kolmogorov Equation ◽  
Initial Boundary Value ◽  
Continuous Dependence On Data

AbstractThis paper is concerned with the continuous dependence of mild solutions on initial values and orders for a general class of initial boundary-value problem to fractional extended Fisher–Kolmogorov equation. The results obtained in this paper can be considered as a contribution to this emerging field.

Sign in / Sign up

Export Citation Format

Share Document