Related papers: Introduction to inverse problems for hyperbolic PD…
This paper develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an actuator at one…
We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient coefficient, in a second-order hyperbolic equation defined on…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
We develop methods for the solution of inhomogeneous Robin type boundary value problems (BVPs) that arise for certain linear parabolic Partial Differential Equations (PDEs) on a half line, as well as a second order generalisation. We are…
A convexification-based numerical method for a Coefficient Inverse Problem for a parabolic PDE is presented. The key element of this method is the presence of the so-called Carleman Weight Function in the numerical scheme. Convergence…
In this paper we propose a reduction procedure for determining generalized travelling waves for first order quasilinear hyperbolic nonhomogeneous systems. The basic idea is to look for solutions of the governing model which satisfy a…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…
This paper is concerned with boundary integral equation methods for solving the two-dimensional fluid-solid interaction problem. We reduce the problem to three differential systems of boundary integral equations via direct and indirect…
This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…
This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…
The challenge of constructing feedback control laws for risk-averse optimal control of partial differential equations (PDEs) with random coefficients is addressed. The control objective composes a tracking-type cost with the nonlinear…
This paper provides a methodology of verified computing for solutions to 1-dimensional advection equations with variable coefficients. The advection equation is typical partial differential equations (PDEs) of hyperbolic type. There are few…
We consider an obstacle problem for (possibly non-local) wave equations, and we prove existence of weak solutions through a convex minimization approach based on a time discrete approximation scheme. We provide the corresponding numerical…
The present paper develops an optimal linear quadratic boundary controller for $2\times2$ linear hyperbolic partial differential equations (PDEs) with actuation on only one end of the domain. First-order necessary conditions for optimality…
In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\geq 3$. In particular the so called the interior determination problem. This non-linear wave…