Related papers: Spectral Boundary Observer for Counter-Flow Heat E…
We propose an observer design for a cascaded system composed of an arbitrary nonlinear ordinary differential equation (ODE) with a 1D heat equation. The nonlinear output of the ODE imposes a boundary condition on one side of the heat…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…
We provide a stochastic fractional diffusion equation description of energy transport through a finite one-dimensional chain of harmonic oscillators with stochastic momentum exchange and connected to Langevian type heat baths at the…
This work is aimed at the study and analysis of the heat transport on a metal bar of length $L$ with a solid-solid interface. The process is assumed to be developed along one direction, across two homogeneous and isotropic materials.…
The paper is devoted to the observability study of a dynamic system, which describes the vibrations of an elastic beam with an attached rigid body and distributed control actions. The mathematical model is derived using Hamilton's principle…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
A popular approach to designing finite-dimensional boundary controllers for partial differential equations (PDEs) is to decompose the PDE into independent modes and focus on the dominant ones while neglecting highly damped residual modes.…
We study coupled non-linear parabolic equations for a fluid described by a material density and a temperature, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on…
This paper presents an adaptive observer design for semilinear hyperbolic rolling contact ODE-PDE systems with uncertain friction characteristics parameterized by a matrix of unknown coefficients appearing in the nonlinear (and possibly…
This paper presents boundary observer design for space and time dependent reaction-advection-diffusion equations using backstepping method. The method uses only a single measurement at the boundary of the systems. The existence of the…
Heat rectifiers would facilitate energy management operations such as cooling, or energy harvesting, but devices of practical interest are still missing. Understanding heat rectification at a fundamental level is key to help us find or…
The dispersion error is often the dominant error for computed solutions of wave propagation problems with high-frequency components. In this paper, we define and give explicit examples of $\alpha$-dispersion-relation-preserving schemes.…
This is the second part of four series papers, aiming at the problem of sensor dynamics compensation for abstract linear systems. Two major issues are addressed. The first one is about the sensor dynamics compensation in system observation…
This paper investigates the output feedback stabilization of parabolic equation with Lipschitz nonlinearity over general multidimensional domain using spectral geometry theories. First, a novel nonlinear observer is designed, and the error…
This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…
In this paper we consider a tank containing fluid and we want to estimate the horizontal currents when the fluid surface height is measured. The fluid motion is described by shallow water equations in two horizontal dimensions. We build a…
In this paper, we introduce a model for a buoyancy-driven, air-to-air heat exchanger. This model, derived from first principles, features a conservative boundary condition at inflow based on the compressible Bernoulli equation, and a…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement…