Related papers: The damped wave equation with unbounded damping
We consider the inverse problem of determining an electromagnetic potential appearing in an infinite cylindrical domain from boundary measurements. More precisely, we prove the stable recovery of some general class of magnetic field and…
In this paper, we consider the problem of nonlinear (in particular, saturated) stabilization of the high-dimensional wave equation with Dirichlet boundary conditions. The wave dynamics are subject to a dissipative nonlinear velocity…
In this paper, we study the asymptotic stability of two wave equations coupled by velocities of anti-symmetric type via only one damping. We adopt the frequency domain method to prove that the system with smooth initial data is…
In this paper, we observe how the heat equation in a non-cylindrical domain can arise as the asymptotic limit of a parabolic problem in a cylindrical domain, by adding a potential that vanishes outside the limit domain. This can be seen as…
This work explores the global existence and scattering behavior of solutions to a damped, inhomogeneous nonlinear Schrodinger equation featuring a time-dependent damping term, an inverse-square potential, and an inhomogeneous nonlinearity.…
We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates.…
This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.
We consider a degenerate/singular wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a…
With asymptotic method developed from weak turbulent theory, the kinetic equations for QGP are expanded in fluctuation field potential $A^T_\mu $. Considering the second-order and third-order currents, we derive the nonlinear permeability…
We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to $\Gamma$-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under…
Following the previous work [1], we investigate the impact of damping on the oscillation of smooth solutions to some kind of quasilinear wave equations with Robin and Dirichlet boundary condition. By using generalized Riccati transformation…
Spectral singularities and the coherent perfect absorption are two interrelated concepts that have originally been introduced and studied for linear waves interacting with complex potentials. In the meantime, the distinctive asymptotic…
A classic no-go theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such…
Damping typically results in attenuation of vibrations and elastic wave propagation in mechanical systems. Contrary to this conventional understanding, we demonstrate experimentally and explain theoretically the revival of an elastic wave…
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…
We study the response of a semi-bounded one-component fully degenerate electron plasma to an initial perturbation in the electrostatic limit. We show that the part of the electric potential corresponding to surface waves in such plasma can…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We analyze the asymptotic dynamics of quasilinear parabolic equations when solutions may grow up (i.e., blow up in infinite time). For such models, there is a global attractor which is unbounded and the semiflow induces a nonlinear dynamics…
The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in…
In this paper we consider an initial-boundary value problem related to some network dynamics where the underlying graph has unbounded edges. We show that there exists a C0-semigroup for this problem using a general result from the…