Related papers: On the stabilization of a hyperbolic Stokes system…
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Without imposing any hypotheses on the structural properties of the damping term, we identify logarithmic decay of solutions with growing…
We study the Stokes-transport system in a two-dimensional channel with horizontally moving boundaries, which serves as a reduced model for oceanography and sedimentation. The density is transported by the velocity field, satisfying the…
We analyse dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a previous known sufficient condition for exponential stability with respect to the C^1-norm is optimal. In particular a known…
A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast…
This paper is concerned with the stability of steady solutions to initial-boundary-value problems of reaction-hyperbolic systems for axonal transport. Under proper structural assumptions, we clarify the relaxation structure of the…
This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima-Shizuta…
Experiments show that isochoric (constant-volume) conditions enhance supercooling stability relative to isobaric (constant-pressure) conditions. Here, combining Helmholtz equilibrium thermodynamics with a first-order perturbation…
We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g. the inviscid Burgers equation for the simple exclusion process. The physical solutions of…
For the 3D Navier-Stokes-Maxwell problem on the whole space and in the presence of external time-periodic forces, first we study the existence of time-periodic small solutions, and then we prove their asymptotic stability. We use new type…
We develop a Nitsche fictitious domain method for the Stokes problem starting from a stabilized Galerkin finite element method with low order elements for both the velocity and the pressure. By introducing additional penalty terms for the…
We are concerned with quasilinear symmetrizable partially dissipative hyperbolic systems in the whole space $\mathbb{R}^d$ with $d\geq2$. Following our recent work [10] dedicated to the one-dimensional case, we establish the existence of…
The problem of constrained stabilization on the n-sphere under star-shaped constraints is considered. We propose a control strategy that allows to almost globally steer the state to a desired location while avoiding star-shaped constraints…
Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in…
The existence and uniqueness of weak solutions is shown for a system related to the Willis model of elastodynamics. Both the whole space case and the case of a bounded smooth domain are studied. To this end the equations are reformulated as…