Decay of solutions of a higher order multidimensional nonlinear Korteweg–de Vries–Burgers system

1994 ◽  
Vol 124 (2) ◽  
pp. 263-271 ◽  
Author(s):  
Zhang Linghai
Keyword(s):  
Initial Value Problem ◽  
Higher Order ◽  
Decay Estimates ◽  
Initial Value ◽  
Decay Of Solutions ◽  
De Vries ◽  
Integral Estimation ◽  
Burgers System

We study decay estimates for the solutions to the initial value problem for a higher order multidimensional nonlinear Korteweg–de Vries–Burgers system. The method is integral estimation.

Optimal L 2 -decay of solutions to a cubic dissipative nonlinear Schrödinger equation

2021 ◽  
pp. 1-13
Author(s):  
Kita Naoyasu ◽  
Sato Takuya
Keyword(s):  
Sobolev Space ◽  
Global Solution ◽  
Initial Value Problem ◽  
Trivial Solution ◽  
Decay Estimate ◽  
Weighted Sobolev Space ◽  
The Other ◽  
Initial Value ◽  
Decay Of Solutions ◽  
Dissipative Nonlinearity

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D Schrödinger equations containing a long-range dissipative nonlinearity, i.e., λ | u | 2 u. Our aim is to obtain the two results. One asserts that, if the L 2 -norm of a global solution, with an initial datum in the weighted Sobolev space, decays at the rate more rapid than ( log t ) − 1 / 2 , then it must be a trivial solution. The other asserts that there exists a solution decaying just at the rate of ( log t ) − 1 / 2 in L 2 .

scholarly journals On the Korteweg–de Vries equation: Frequencies and initial value problem

1997 ◽  
Vol 181 (1) ◽  
pp. 1-55 ◽  
Author(s):  
D. Bättig ◽  
T. Kappeler ◽  
B. Mityagin
Keyword(s):  
Initial Value Problem ◽  
Vries Equation ◽  
Initial Value ◽  
De Vries

scholarly journals Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 809
Author(s):  
Aissa Boukarou ◽  
Kaddour Guerbati ◽  
Khaled Zennir ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Unique Solution ◽  
Initial Value Problem ◽  
Coupled System ◽  
Well Posedness ◽  
Initial Value ◽  
Gevrey Spaces ◽  
De Vries ◽  
Gevrey Space

Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisting of modified Korteweg-de Vries equations for given data. Furthermore, we prove that the unique solution belongs to Gevrey space G σ × G σ in x and G 3 σ × G 3 σ in t. This article is a continuation of recent studies reflected.

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