In this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation u′′ −M(t, ‖u(t)‖)∆u+ |u| = f in Ω× (0, T0), u = 0 on Γ0×]0, T0[, ∂u ∂ν + δh(u′) = 0 on Γ1×]0, T0[, where Ω is a bounded domain of Rn with its boundary constiting of two disjoint parts Γ0 and Γ1; ρ > 1 is a real number; ν(x) is the exterior unit normal vector...

Abstract This work is devoted to studying a viscoelastic Kirchhoff-type equation with nonlinear boundary damping-source interactions in bounded domain. Under suitable assumptions on the kernel function g , density function, and M global existence general decay rate of solution are established. Moreover, we prove finite time blow-up result negative initial energy.

The fundamental relationship between matrices over the rational numbers and a newly defined type of graph, a Kirchhoff graph, is discussed. For a given matrix, a Kirchhoff graph for that matrix represents the orthogonal complementarity of the null and row spaces of the matrix. A number of basic results are proven, and then a relatively complicated Kirchhoff graph is constructed for a matrix tha...

A class of Kirchhoff type systems with nonlinear boundary conditions considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameters are small enough.

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow fie ld are modeled with the aid of Spalart-Alimaras one-equation turbulence modeL Appropriate acoustic and outflow boundary conditions were implemented to ...

Abstract In this paper, we investigate the existence of a least-energy sign-changing solutions for following Kirchhoff-type equation: $$ - \biggl(1+b \int _{\mathbb{R}^{2}} K(x) \vert \nabla u ^{2}\,dx \biggr) \operatorname{div} \bigl(K(x)\nabla \bigr)=K(x)f(u),\quad x\in \mathbb{R}^{2}, − ( <...

The present paper deals with a Kirchhoff problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R^{N}. The problem studied is a stationary version of the orig inal Kirchhoff equation, involving the p(x)-Lap lacian operator, in the framework of the variable exponent Lebesgue and Sobolev spaces. The question of the existence of weak solutions is treated. Appl...