In this paper, active disturbance rejection control (ADRC) approach is used to stabilize a 2×2 system of first-order linear hyperbolic partial differential equations (PDEs) subject to a boundary input disturbance. Disturbance attenuation is achieved with the designed controller, and the resulting closed-loop control system admits a unique solution, which could tend to any arbitrary vicinity of ...

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem have been proposed and tested numerically on a number examples PDEs. This has given rise lively field research which methods related Monte Carlo are In article ...

Abstract We introduce Fireshape, an open-source and automated shape optimization toolbox for the finite element software Firedrake. Fireshape is based on moving mesh method allows users with minimal knowledge to tackle ease challenging problems constrained partial differential equations (PDEs).

We apply a version of the dressing method to a system of four dimensional nonlinear Partial Differential Equations (PDEs), which contains both Pohlmeyer equation (i.e. nonlinear PDE integrable by the Inverse Spectral Transform Method) and nonlinear matrix PDE integrable by the method of characteristics as particular reductions. Some other reductions are suggested.

A method for the discretization of the Boltzmann equation in velocity space via a Galerkin procedure with Hermite polynomials as trial and test functions is proposed. This procedure results in a set of partial differential equations, which is an alternative to the lattice-Boltzmann equations. These PDEs are discretized using an explicit finite difference scheme and a numerical example shows the...

This paper considers the optimal control and optimal estimation problems for a class of linear parabolic diffusion-reaction partial differential equations (PDEs) with actuators and sensors at the boundaries. Diffusion-reaction PDEs with boundary actuation and sensing arise in a multitude of relevant physical systems (e.g. magneto-hydrodynamic flows, chemical reactors, and electrochemical conver...

Finding the general solution of partial differential equations (PDEs) is essential for controller design in newly developed methods. Interconnection and damping assignment passivity-based control (IDA-PBC) one such methods which to corresponding PDEs are called matching needed apply it practice. In this paper, these transformed Pfaffian equations. Furthermore, shown that upon satisfaction integ...

Short review of an approach to explicit solving of initial and boundary value problems (BVPs) for some partial differential equations (PDEs) is presented. A combination of two classical methods Å the Fourier method and the Duhamel principle Å is used in the framework of a two-dimensional operational calculus. It gives explicit solutions of some local and nonlocal BVPs for the classical equation...

We are concerned with free boundary problems arising from the analysis of multidimensional transonic shock waves for Euler equations in compressible fluid dynamics. In this expository paper, we survey some recent developments and corresponding related nonlinear partial differential (PDEs) mixed type. The PDEs under our include steady potential flow, full equations, unsteady elliptic–hyperbolic ...