SOLUTIONS OF THE BOUSSINESQ EQUATION ON A PERIODIC DOMAIN

被引:13
作者
LIU, FL [1 ]
RUSSELL, DL [1 ]
机构
[1] VIRGINIA POLYTECH INST & STATE UNIV,DEPT MATH,BLACKSBURG,VA 24061
关键词
D O I
10.1006/jmaa.1995.1167
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The existence and the uniqueness of solutions for a linear feedback controlled Boussinesq equation on a periodic domain are studied. The continuous dependence of the solution on initial data is also proved. The proof is based on conservation laws for the Boussinesq equation. (C) 1995 Academic Press, Inc.
引用
收藏
页码:194 / 219
页数:26
相关论文
共 39 条
[1]   DECAY OF SOLUTIONS OF SOME NONLINEAR-WAVE EQUATIONS [J].
AMICK, CJ ;
BONA, JL ;
SCHONBEK, ME .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 81 (01) :1-49
[3]   ON THE EXISTENCE OF SOLUTIONS TO THE EQUATION UTT = UXXT + SIGMA-(UX)X [J].
ANDREWS, G .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1980, 35 (02) :200-231
[4]  
BENJAMIN TB, 1972, PHIL T R SOC LONDO A, V47, P72
[5]   SOLUTIONS OF KORTEWEG-DEVRIES EQUATION IN FRACTIONAL ORDER SOBOLEV SPACES [J].
BONA, J ;
SCOTT, R .
DUKE MATHEMATICAL JOURNAL, 1976, 43 (01) :87-99
[6]   GLOBAL EXISTENCE OF SMOOTH SOLUTIONS AND STABILITY OF SOLITARY WAVES FOR A GENERALIZED BOUSSINESQ EQUATION [J].
BONA, JL ;
SACHS, RL .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 118 (01) :15-29
[7]   INITIAL-VALUE PROBLEM FOR KORTEWEG-DEVRIES EQUATION [J].
BONA, JL ;
SMITH, R .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1975, 278 (1287) :555-601
[8]  
Boussine J., 1872, J MATH PURE APPL, V17, P55
[9]   DECAY-ESTIMATES FOR SOME SEMILINEAR DAMPED HYPERBOLIC PROBLEMS [J].
HARAUX, A ;
ZUAZUA, E .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1988, 100 (02) :191-206
[10]  
HARAUX A, 1981, LECTURE NOTES MATH, V841