相关论文: Polynomial Stability of an Elastic Thin Plate on N…

For the stationary hydrodynamic model for semiconductors with sonic boundary, represented by Euler-Poisson equations, it possesses the various physical solutions including interior subsonic solutions/interior supersonic solutions/shock…

We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of…

This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…

We observe a dramatic lack of robustness of the DPG method when solving problems on large domains and where stability is based on a Poincar\'e-type inequality. We show how robustness can be re-established by using appropriately scaled test…

Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal…

With a small parameter $\epsilon$, Poisson-Nernst-Planck (PNP) systems over a finite one-dimensional (1D) spatial domain have steady state solutions, called 1D boundary layer solutions, which profiles form boundary layers near boundary…

We discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examples of stickiness can be obtained only by removing the…

We prove the local well-posedness of the 3D free-boundary incompressible elastodynamics with surface tension describing the motion of an elastic medium in a periodic domain with a moving graphical surface. The deformation tensor is assumed…

This paper considers the problem of learning control laws for nonlinear polynomial systems directly from the data, which are input-output measurements collected in an experiment over a finite time period. Without explicitly identifying the…

The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…

We investigate one- and multi-dimensional stability of noncharacteristic boundary layers in the limit approaching a standing planar shock wave $\bar U(x_1)$, $x_1>0$, obtaining necessary conditions of (i) weak stability of the limiting…

We consider a pointwise stabilization problem for a coupled wave and plate equations. We prove under rather general assumptions, that such systems can stabilized so as to have arbitrarily high decay rates and are exactly controllable. We…

The electrostatic stability of electron-positron plasmas is investigated in the point-dipole and Z-pinch limits of dipole geometry. The kinetic dispersion relation for sub-bounce-frequency instabilities is derived and solved. For the…

An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By…

We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…

In this note, we showcase some recent results concerning the stickiness properties of nonlocal minimal graphs in the plane. To start with, the nonlocal minimal graphs in the plane enjoy an enhanced boundary regularity, since boundary…

The linear stability of a stratified shear flow for smooth density profiles is studied. This work focuses on the nature of the stability boundaries of flows in which both Kelvin-Helmholtz and Holmboe instabilities are present. For a fixed…

Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a…

This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design…

The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…