In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with acoustic boundary in a bounded domain in Rn. To stabilize the system, we incorporate separately, the passive viscous damping in the model as like Gannesh C. Gorain [1]. Energy decay rate is obtained by the exponential stability of solutions by using multiplier technique.

In this article, we are interested in the existence of positive solutions for the following Kirchhoff type system  −M1 (∫ Ω |x| −ap|∇u|p dx ) div(|x|−ap|∇u|p−2∇u) = λ|x|−(a+1)p+c1 (f(v)− 1 uα ) in Ω, −M2 (∫ Ω |x| −bq |∇v|q dx ) div(|x|−bq |∇v|q−2∇v) = λ|x|−(b+1)q+c2 (g(u)− 1 vβ ) in Ω, u = v = 0 on ∂Ω, (1) where Ω is a bounded smooth domain of R with 0 ∈ Ω, 1 < p, q < N , 0 ≤ a, b < N−p p , c...

We consider the curve straightening flow of inextensible, open, planar curves generated by the Kirchhoff bending energy. It can be considered as a model for the motion of elastic, inextensible rods in a high friction regime. We derive governing equations, namely a semilinear fourth order parabolic equation for the indicatrix and a second order elliptic equation for the Lagrange multiplier. We p...

We present some general bounds for the algebraic and geometric multiplicity of eigenvalues of second order elliptic operators on finite networks under continuity and weighted Kirchhoff flow conditions at the vertices. In particular the algebraic multiplicity of an eigenvalue is shown to be strictly bounded from above by the number of vertices if there are no eigenfunctions vanishing in all node...

We show under mild assumptions that a composition of internally well-posed, impedance passive (or conservative) boundary control systems through Kirchhoff type connections is also an internally well-posed, impedance passive (resp., conservative) boundary control system. The proof is based on results of [21]. We also present an example of such composition involving Webster’s equation on a Y-shap...

We consider a quasilinear elliptic transmission problem where the nonlinearity changes discontinuously across two subdomains. By a reformulation of the problem via Kirchhoff transformation we first obtain linear problems on the subdomains together with nonlinear transmission conditions and then a nonlinear Steklov– Poincaré interface equation. We introduce a Dirichlet–Neumann iteration for this...

Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...