Related papers: Spectral Boundary Observer for Counter-Flow Heat E…
The present work is devoted to the problem of boundary stabilization of the semilinear 1-D heat equation with nonlocal boundary conditions. The stabilizing controller is finite-dimensional, linear, given in an explicit form, involving only…
This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's…
We present a set of new energy-stable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. These boundary conditions are developed through two steps: (i)…
A Spectral Difference (SD) algorithm on tensor-product elements which solves the reacting compressible Navier-Stokes equations (NSE) is presented. The classical SD algorithm is shown to be unstable when a multispecies gas where…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
Robust output tracking is addressed in this paper for a heat equation with Neumann boundary conditions and anti-collocated boundary input and output. The desired reference tracking is solved using the well-known flatness and Lyapunov…
Transmission spectroscopy is a key technique in the characterization of exoplanet atmospheres and has been widely applied to planets undergoing hydrodynamic escape. While a robust analytic theory exists for transmission spectra of…
Inverse Stefan problem arising in modeling of laser ablation of biomedical tissues is analyzed, where information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the…
In adaptive control, a controller is precisely designed for a certain model of the system, but that model's parameters are updated online by another mechanism called the adaptive update. This allows the controller to aim for the benefits of…
This paper presents the control design of the two-phase Stefan problem. The two-phase Stefan problem is a representative model of liquid-solid phase transition by describing the time evolutions of the temperature profile which is divided by…
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable,…
We show that a steady-state solution ${\bf U}$ to the system of equations of a Navier-Stokes flow past a rotating body is nonlinearly unstable if the associated linear operator $\cal L$ has a part of the spectrum in the half-plane…
This paper develops an input-to-state stability (ISS) analysis of the Stefan problem with respect to an unknown heat loss. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a…
We present a methodology for designing bilateral boundary controllers for a class of systems consisting of a coupled diffusion equation with an unstable ODE at an arbitrary interior point. A folding transformation is applied about the…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
This paper presents results for the sampled-data boundary feedback control to the Stefan problem. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile…
The problem of unknown input observer design is considered for coupled PDE/ODE systems subject to incremental sector bounded nonlinearities and unknown boundary inputs. Assuming available measurements at the boundary of the distributed…
We consider change point detection for the volatility in second order linear parabolic stochastic partial differential equations based on high frequency spatio-temporal data. We give a test statistic to detect changes in the volatility…
The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about $0$ along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance…
We establish uniqueness and stability inequalities for the problem of determining the higher-order coefficients of an elliptic operator from the corresponding boundary spectral data (BSD). Our analysis relies on the relationship between…