In this paper, modulating functions-based method is proposed for estimating space–time-
dependent unknowns in one-dimensional partial differential equations. The proposed …

In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied
to the inverse time-dependent force function in the wave equation on regular and irregular …

In this paper, we propose a non-asymptotic state estimation method for the linear reaction
diffusion equation with general boundary conditions. The method is based on the …

In this paper, a non-asymptotic state estimation method for a class of nonlinear partial
differential equations with general boundary conditions is presented. The method combines …

Many systems with distributed dynamics are described by partial differential equations
(PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The …

In the present work we derive and study a non-linear elliptic PDE coming from the problem
of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to …

In this paper, a non-asymptotic and robust method is proposed for the joint estimation of time-
delay and fault for a class of time-delayed reaction diffusion equations with general …

This paper is devoted to the study of an inverse problem of recovering a space-dependant
source term in a Sobolev-type equation from final measurement data. The aim of this work is …

This master thesis is devoted to the state estimation of a particular form of PDE systems,
coupled parabolic PDEs with spatial dependent coefficients. This form of PDEs represent …

Observers are well known in the theory of dynamical systems. They are used to estimate the
states of a system from some measurements. However, recently observers have also been …