Solutions to ocean acoustic scattering problems are often formulated in the frequency domain, which implies that the surface is "frozen" in time. This may be reasonable for short duration signals but breaks down if the surface changes appreciably over the transmission time. Frequency domain solutions are also impractical for source-receiver ranges and frequency bands typical for applications su...

"In this paper, we consider a nonlinear $p-$Kirchhoff type hyperbolic equation with damping and source terms $$u_{tt}-M\left( \underset{\Omega }{\int }\left\vert \nabla u\right\vert ^{p}dx\right) \Delta _{p}u+\left\vert u_{t}\right\vert ^{m-2}u_{t}=\left\vert ^{r-2}u.$$ Under suitable assumptions positive initial energy, prove the global existence of solution by using potential energy Nehari's ...

The second Rayleigh-Sommerfeld (RS) diffraction integral, wherein the normal derivative is specified, is evaluated in simple closed form for all axial points when a divergent or convergent spherical wave is incident upon a circular aperture or disk. These evaluations (solutions) are compared with known corresponding solutions of the first RS diffraction integral. These sets of solutions are int...

‎Using Nehari manifold methods and Mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.

The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. Its considerable applications are found in a variety of fields. In this paper, we determine the maximum value of Kirchhoff index among the unicyclic graphs with fixed number of vertices and maximum degree, and characterize the corresponding extremal graph.

A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4). 1 A new integrable case for the Kirchhoff equation. The Kirchhoff equations (see for example [1]) for the motion of a rigid body in an ideal fluid read as follows M t = M × ∂H ∂M + Γ × ∂H ∂Γ , Γ t = Γ × ∂H ∂M ,

It is well-known that natural surfaces can be very accurately described in terms of fractal geometry. In fact, natural surfaces exhibit statistical scale-invariance properties that are very well modeled by using the 2D fractional Brownian motion (fBm) stochastic process. Therefore, for all of the applications in which it is of interest to compute the electromagnetic scattering from natural surf...

We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation sche...