Offset continuation (OC) is the operator that transforms common-offset seismic reflection data from one offset to another. Earlier papers by the first author presented a partial differential equation in midpoint and offset to achieve this transformation. The equation was derived from the kinematics of the continuation process. This derivation is equivalent to proposing the wave equation from kn...

We investigate the well-posedness, the exponential stability, or the lack thereof, of thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial boundary value problems for different boundary conditions deal with systems of partial differential equations in...

This article concerns the existence of sign-changing solutions to nonlocal Kirchhoff type problems of the form

"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 ...

We show the presence of a dense pure point spectrum on quantum graphs with Maryland-type quasiperiodic Kirchhoff coupling constants at the vertices.

In this paper, we derive a sharp observability inequality for Kirchhoff plate equations with lower order terms in an unbounded domain Ω of lR. More precisely, when the observation is assumed to be located in a subdomain ω such that Ω \ ω is bounded and the observation time T > 0 is sufficiently large, we establish an observability estimate with an explicit observability constant for Kirchhoff p...