Variational Methods in Semilinear Wave Equation with Nonlinear Boundary Conditions and Stability Questions

被引：1

作者：

Nowakowski, A. ^{[1
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Banacha 22, PL-90238 Lodz, Poland

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2018年 / 30卷 / 01期

关键词：

Dual variational method; Semi-linear wave equation; Dissipation and sources term on the boundary; STATE CONSTRAINTS; HYPERBOLIC-EQUATIONS; PARABOLIC-SYSTEMS; DAMPING TERMS; UNIFORM DECAY; BLOW-UP; EXISTENCE; INSTABILITY; RATES;

D O I：

10.1007/s10884-016-9531-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present variational approach to the semilinear equation of the vibrating string x(tt)(t, y) - Delta x(t, y) + l(t, y, x(t, y)) = 0 in bounded domain and certain type of nonlinearity on the boundary. To this effect we derive new dual variational method. Next the question of stability of solutions with respect to initial conditions is discussed.

引用

页码：117 / 134

页数：18

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