Related papers: Inverse Conduction Problem for a Parabolic Equatio…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
In this paper the approximate solution of the heat exchange problem by A.N. Tikhonov regularization method is presented. The errror estimation of this approximate is obtained.
We present a frequency domain based $H_\infty$-control strategy to solve boundary control problems for systems governed by parabolic or hyperbolic partial differential equation, where controllers are constrained to be physically…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
In this article, for an advection-diffusion equation we study an inverse problem for restoration of source temperature from the information of final temperature profile. The uniqueness of this inverse problem is established by taking an…
We develop an embedded boundary method (EBM) to solve the two-phase incompressible flow with piecewise constant density. The front tracking method is used to track the interface. The fractional step methods are used to solve the…
In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…
The extraction problem of information about the location and shape of the cavity from a single set of the temperature and heat flux on the boundary of the conductor and finite time interval is a typical and important inverse problem. Its…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown…
We prove new bounds on the heat flux out of the bottom boundary, $\mathcal{F}_B$, for a fluid at infinite Prandtl number, heated internally between isothermal parallel plates under two kinematic boundary conditions. In uniform internally…
This work studies the inverse boundary problem for the two photon absorption radiative transport equation. We show that the absorption coefficients and scattering coefficients can be uniquely determined from the \emph{albedo} operator. If…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
By a probabilistic method we provide an explicit fundamental solution of the Cauchy problem associated to the heat equation on the half-line with constant drift and Dirichlet boundary condition at zero.
Quantifying irreversibility of a system using finite information constitutes a major challenge in stochastic thermodynamics. We introduce an observable that measures the time-reversal asymmetry between two states after a given time lag. Our…
We study a time-reversed hyperbolic heat conduction problem based upon the Maxwell--Cattaneo model of non-Fourier heat law. This heat and mass diffusion problem is a hyperbolic type equation for thermodynamics systems with thermal memory or…
We obtain an analytical bound on the mean vertical convective heat flux $\langle w T \rangle$ between two parallel boundaries driven by uniform internal heating. We consider two configurations, one with both boundaries held at the same…
Let $\Omega\subset\R^n$, $n\ge 3$, be a smooth bounded domain and consider a coupled system in $\Omega$ consisting of a conductivity equation $\nabla \cdot \gamma(x) \nabla u(t,x)=0$ and an anisotropic heat equation…
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic…