Related papers: Boundary stabilization of a vibrating string with …
In this paper we study the stability of two different problems. The first one is a one-dimensional degenerate wave equation with degenerate damping, incorporating a drift term and a leading operator in non-divergence form. In the second…
We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based…
We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with…
We study the spectral problem associated with the equation governing the small transverse motions of a viscoelastic tube of finite length conveying an ideal fluid. The boundary conditions considered are of general form, accounting for a…
We consider the damped wave equation with Dirichlet boundary conditions on the unit square. We assume the damping to be a characteristic function of a strip. We prove the exact $t^{-4/3}$-decay rate for the energy of classical solutions.…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
We consider the phase transition of a string with tension $\eps_1$ to a string with a smaller tension $\eps_2$ at finite temperature. For sufficiently small temperatures the transition proceeds through thermally catalyzed quantum tunneling,…
In [V. Barcilon Explicit solution of the inverse problem for a vibrating string. J. Math. Anal. Appl. {\bf 93} (1983) 222-234] two boundary value problems were considered generated by the differential equation of a string $$…
In this paper, we prove the optimal lower bound $\frac{\lambda_n}{\lambda_m}\geq(\frac{n}{m})^2$ of vibrating string $$-y''=\lambda\rho(x) y,$$ with Dirichlet boundary conditions for concave densities. Our aproach is based on the method of…
The determination of an unknown spacewice dependent force function acting on a vibrating string from over-specified Cauchy boundary data is investigated numerically using the boundary element method (BEM) combined with a regularized method…
We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. We show that if the damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the boundary…
We consider a damped wave equation in a bounded domain. The damping is nonlinear and is homogeneous with degree p -- 1 with p > 2. First, we show that the energy of the strong solution in the supercritical case decays as a negative power of…
The behavior of the average energy for an ensemble of non-interacting particles is studied using scaling arguments in a dissipative time-dependent stadium-like billiard. The dynamics of the system is described by a four dimensional…
In this paper, we investigate pulsating string solutions within the context of a two-parameter $\chi$-deformed $\mathcal{R} \times S^2$ background. We derive the energy and oscillation number relation for the deformed $\mathcal{R} \times…
In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\cite{AW} to affirm the…
Hydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low-Reynolds-number are investigated within the point-particle model. Evolution of a benchmark initial configuration is studied,…
We give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is…
We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to…
We provide estimates for the asymptotic gains of the displacement of a vibrating string with endpoint forcing, modeled by the wave equation with Kelvin-Voigt and viscous damping and a boundary disturbance. Two asymptotic gains are studied:…
An $(n, 1)$ string is a bound state of a D-string and $n$ fundamental strings. It may be described by a D-string with a world volume electric field turned on. As the electric field approaches its critical value, $n$ becomes large. We…