On the weak solutions and persistence properties for the variable depth KDV general equations

被引：2

作者：

Fan, Lili ^{[1
]}

Yan, Wei ^{[1
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 44卷

关键词：

Variable depth KDV general equations; Weak solution; Persistence property; Generalized Gronwall's inequalities; LOCAL WELL-POSEDNESS; SHALLOW-WATER WAVES; FORNBERG-WHITHAM EQUATION; CAMASSA-HOLM EQUATION; MODEL EQUATION; BREAKING WAVES; EXISTENCE; CONTINUITY; UNIQUENESS;

D O I：

10.1016/j.nonrwa.2018.05.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Considered in this paper is a nonlinear evolution equation for surface waves in shallow water over uneven bottom. Due to the dependence on the bottom function of the coefficients and its involved complicated structure of the equation, the generalized Gronwall's inequalities are proposed to be used to derive the required priori estimates, with which, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space H-s(R) with 1 < s <= 3/2 is obtained. Moreover, the persistence properties in weighted L-phi(P)= L-P (R, phi(P)dx) spaces on strong solutions are also investigated. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：223 / 245

页数：23

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