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We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…
We study partial data inverse problems for linear and nonlinear parabolic equations with unknown time-dependent coefficients. In particular, we prove uniqueness results for partial data inverse problems for semilinear reaction-diffusion…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
In this paper we utilise new methods of Calculus of Variations in $L^\infty$ to provide a regularisation strategy to the ill-posed inverse problem of identifying the source of a non-homogeneous linear elliptic equation, satisfying Dirichlet…
We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…
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…
An inverse problem to identify unknown coefficients of a partial differential equation by a single interior measurement is considered. The equation considered in this paper is a strongly elliptic second order scalar equation which can have…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
The ability to measure polarisation, spectrum, temporal dynamics, and spatial amplitude and phase of optical beams is essential to study fundamental phenomena in laser dynamics, telecommunications and nonlinear optics. Current…
This article considers nonlocal heat flows into a singular target space. The problem is the parabolic analogue of a stationary problem that arises as the limit of a singularly perturbed elliptic system. It also provides a gradient flow…
In this paper, we establish a necessary and sufficient condition for the existence and regularity of the density of the solution to a semilinear stochastic (fractional) heat equation with measure-valued initial conditions. Under a mild cone…
We consider the identifiability and stable numerical estimation of multiple parameters in a Cahn-Hilliard model for phase separation. Spatially resolved measurements of the phase fraction are assumed to be accessible, with which the…
In the first part of this paper, we prove the global regularity, in an adequate parabolic Bessel-Potential space and then in the corresponding parabolic fractional Sobolev space, of the unique solution to following fractional heat equation…
In this paper, a new inverse identification method is developed from full kinematic and thermal field measurements. It consists in reconstructing the heat source from two approaches, a first one that requires the measurement of the…
We consider nonnegative solutions of the quasilinear heat equation $\partial_t u = \tfrac{1}{2} u \partial_x^2 u$ in one dimension. Our solutions may vanish and may be unbounded. The equation is then degenerate, and weak solutions are…
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…
Source identification problems have multiple applications in engineering such as the identification of fissures in materials, determination of sources in electromagnetic fields or geophysical applications, detection of contaminant sources,…