Well-posedness for a class of mixed problem of wave equations

被引：1

作者：

Liu, Haihong ^{[1
]}

Su, Ning ^{[2
]}

机构：

[1] Yunnan Normal Univ, Dept Math, Kunming 650092, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 1-2期

关键词：

Well-posedness; Wave equation; Variable separation; Eigenvalue; Energy inequality;

D O I：

10.1016/j.na.2008.10.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies an initial-boundary value problem (IBV) of the wave equation, in which time derivative of second order appears in the boundary condition. This results in study of new Sturm-Liouville problem. The solution of IBV is then constructed in terms of the family of eigenfunctions of the S-L problem. Uniqueness and stability are proved via energy inequality method. Some extension is explained. A parabolic variant is also illustrated. (c) 2008 Elsevier Ltd. All rights reserved.

引用

页码：19 / 27

页数：9

共 10 条

[1]

[Anonymous], 1953, Methods of mathematical physics

[2]

[Anonymous], 2015, Elliptic Partial Differential Equations of Second Order. Classics in Mathematics

[3]

Dautray R, 1988, MATH ANAL NUMERICAL, V5

[4] A comparison theorem for the first non-zero Steklov eigenvalue [J].

Escobar, JF .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 178 (01) :143-155

[5]

KUNMIAO L, 2002, METHODS MATH PHYS

[6]

Lions J. L., 1972, NONHOMOGENEOUS BOUND

[7]

Showalter R. E., 1994, Electron. J. Differ. Equ. Monograph, V1

[8]

THOMOSN WT, 1988, THEORY VIBRATION APP

[9]

TIKHONOV AN, 1967, EQUATIONS MATH PHYS

[10]

Yosida K., FUNCTIONAL ANAL

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