Non-uniform dependence for a generalized Degasperis-Procesi equation
Shaohui Gui, Jinlu Li, Weipeng Zhu
TL;DR
This paper investigates the generalized Degasperis-Procesi equation and demonstrates that the solution map from initial data to solutions is not uniformly continuous, highlighting certain instability properties.
Contribution
It provides a rigorous proof that the data-to-solution map for the generalized Degasperis-Procesi equation lacks uniform continuity.
Findings
Data-to-solution map is not uniformly continuous.
Highlights instability in the solution behavior.
Advances understanding of the equation's mathematical properties.
Abstract
In the paper, we consider the Cauchy problem for a generalized Degasperis-Procesi equation. We prove that the data-to-solution map is not uniformly continuous.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems