The influence of oscillations on global existence for a class of semi-linear wave equations

被引：4

作者：

Ebert, M. R. ^{[2
]}

Reissig, Michael ^{[1
]}

机构：

[1] Tech Univ Bergakad Freiberg, Fac Math & Comp Sci, D-09596 Freiberg, Germany

[2] Univ Sao Paulo, Fac Filosofia Ciencias & Letras Ribeirao Preto, Dept Fis & Matemat, BR-14040901 Ribeirao Preto, SP, Brazil

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2011年 / 34卷 / 11期

基金：

巴西圣保罗研究基金会;

关键词：

semi-linear wave equations; Cauchy problem; second-order wave equations; global existence; small data solutions; BEHAVIOR; PROPAGATION; ENERGY; SPEED;

D O I：

10.1002/mma.1430

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u(tt) - a(t)(2) Delta u = u(t)(2) - a(t)(2)vertical bar del u vertical bar(2). In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions. Copyright c 2011 John Wiley & Sons, Ltd.

引用

页码：1289 / 1307

页数：19

共 15 条

[1] Eastham M.S.P., 1973, The spectral theory of periodic differential equations
[2] GEORGIEV V, 2000, MSJ MEMOIRS, V7
[3] On the asymptotic behavior of the energy for the wave equations with time depending coefficients
Hirosawa, Fumihiko
[J]. MATHEMATISCHE ANNALEN, 2007, 339 (04) : 819 - 838
[4] Generalised energy conservation law for wave equations with variable propagation speed
Hirosawa, Fumihiko
Wirth, Jens
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 358 (01) : 56 - 74
[5] Hormander Lars, 1997, Lectures on nonlinear hyperbolic equations, Mathematiques & Applications, V26
[6] Kubo H, 2005, OPER THEOR, V159, P113
[7] Does the loss of regularity really appear?
Lu, Xiaojun
Reissig, Michael
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2009, 32 (10) : 1246 - 1268
[8] Magnus W., 1966, Hill's equation
[9] REISSIG M, OPTIMALITY IN PRESS
[10] Reissig M., 2000, REND SEM MAT U POLIT, V58, P375

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