Continuous Dependence for the Damped Nonlinear Hyperbolic Equation

Abstract

Abstract-This paper gives the continuous dependence of solutions for the damped nonlinear hyperbolic equation.

Wave-Plate Tipi Denklem Sisteminin Sürekli Bağımlılığı

“…x t ν ∂ = = = ∈ ∂Ω > ∂ (22) Firstly the following theorem establishes continuous dependence of the solution of (1)-(5) on the coefficient µ .…”

“…Theorem 2. Let u and v be the solutions of the problem ( 18)- (22). Then the following estimate holds:…”

Continuous dependence of solutions to double dispersive equation with dissipative term

“…Recently, many important works have been done on deriving estimates about structural stability of the equation. Those of works are examined for multidimensional equations in following main books [1,2], the articles [4,5,[10][11][12][13]19], and references therein.…”

Continuous Dependence For Benjamin-Bona-Mahony-Burger Equation

“…Continuous dependence on coefficients of solutions of partial differential equations is a kind of structural stability that reflects the influence of small changing on coefficient of the solutions of equations. In the recent years, many results of this type can be found in the literature [6][7][8][9][10][11][12][13].…”