VARIATIONAL ANALYSIS OF SEMILINEAR PLATE EQUATION WITH FREE BOUNDARY CONDITIONS

被引：0
|
作者：
Nowakowski, Andrzej [1 ]
机构：
[1] Univ Lodz, Fac Math & Comp Sci, PL-90131 Lodz, Poland
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 07期
关键词：
Dual variational method; semi-linear plate equation; free boundary conditions; nonlinear force; nonlinerity on the boundary; NONLINEAR-WAVE EQUATIONS; UNIFORM DECAY; EXISTENCE;
D O I：
10.3934/dcds.2015.35.3133
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a variational analysis for the semilinear equation of the vibrating plate x(tt)(t, y) + Delta(2)x(t, y) + l(t, y, x(t, y)) = 0 in a bounded domain and a free nonlinear boundary condition Delta x(t, y) = H-x(t, y, x(t, y)) - Q(x)(t, y, x(t, y)). In this context new dual variational methods are developed. Applying a variational approach we discuss a stability of solutions with respect to initial conditions.
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页码：3133 / 3154
页数：22
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