Related papers: Evolution Semigroups in Supersonic Flow-Plate Inte…
Asymptotic-in-time feedback control of a panel interacting with an inviscid, subsonic flow is considered. The classical model [22] is given by a clamped nonlinear plate strongly coupled to a convected wave equation on the half space. In the…
We consider a cantilevered (clamped-free) beam in an axial potential flow. Certain flow velocities may bring about a bounded-response instability in the structure, termed {\em flutter}. As a preliminary analysis, we employ the theory of…
The steady laminar supersonic flow past a flat plate having a stretch of an elastic membrane, the pressure on the other side of which is adjustable, is studied within the framework of the triple deck theory. The resulting lower deck problem…
This paper discusses the mutual interactions between a thin flexible aluminum plate and supersonic flow using two-dimensional (2D) numerical simulations. Calculations are performed using an open source library, SU2, that solves partial…
A partially hinged, partially free rectangular plate is considered, with the aim to address the possible unstable end behaviors of a suspension bridge subject to wind. This leads to a nonlinear plate evolution equation with a nonlocal…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…
The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of…
Generalized Navier-Stokes equations which were proposed recently to describe active turbulence in living fluids are analyzed rigorously. Results on wellposedness and stability in the $L^2(\mathbb{R}^n)$-setting are derived. Due to the…
The motion of a thin elastic plate interacting with a viscous fluid is investigated. A periodic force acting on the plate is considered, which in a setting without damping could lead to a resonant response. The interaction with the viscous…
We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…
We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) full von Karman shallow shell equations that accounts for both…
We consider a nonlinear fourth order in space partial differential equation arising in the context of the modeling of nonlinear acoustic wave propagation in thermally relaxing viscous fluids. We use the theory of operator semigroups in…
Driven systems are of fundamental scientific interest, as they can exhibit properties that are radically different from the same system at equilibrium. In certain cases, long-lived states of driven matter can emerge, which exhibit new…
The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…
We formulate a model for the dynamic growth of a membrane developing in a flow as the result of a precipitation reaction, a situation inspired by recent microfluidic experiments. The precipitating solid introduces additional forces on the…
We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid-structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on…
We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The…
We investigate the steady-state fluid--structure interaction between a Newtonian fluid flow and a deformable microtube in two novel geometric configurations arising in recent microfluidics experiments. The first configuration is a…