Global piecewise classical solutions to quasilinear hyperbolic systems on a tree-like network

被引：0

作者：

Wang, Libin ^{[1
,2
]}

Wang, Ke ^{[3
,4
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, 220 Handan Rd, Shanghai 200433, Peoples R China

[2] Fudan Univ, Lab Math Nonlinear Sci, 220 Handan Rd, Shanghai 200433, Peoples R China

[3] Donghua Univ, Dept Math, 2999 North Renmin Rd, Shanghai 201620, Peoples R China

[4] Donghua Univ, Inst Nonlinear Sci, 2999 North Renmin Rd, Shanghai 201620, Peoples R China

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2022年 / 19卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Quasilinear hyperbolic system; global piecewise classical solution; tree-like network; quasilinear wave equation; EXACT BOUNDARY CONTROLLABILITY; NODAL PROFILE;

D O I：

10.1142/S0219891622500151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the existence, uniqueness and asymptotic stability of global piecewise C-1 solution to the mixed initial-boundary value problem for 1-D quasilinear hyperbolic systems on a tree-like network. Under the assumption of boundary dissipation, when the given boundary and interface functions possess suitably small C-1 norm, we obtain the existence and uniqueness of global piecewise C-1 solution. Moreover, when they further possess a polynomial or exponential decaying property with respect to t, then the corresponding global piecewise C-1 solution possesses the same or similar decaying property. These results will be used to show the asymptotic stability of the exact boundary controllability of nodal profile on a tree-like network.

引用

页码：523 / 548

页数：26

共 13 条

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