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Lyapunov functions are popularly used to investigate the stabilization problem of systems of hyperbolic conservation laws with boundary controls. In real life applications often not every boundary value can be observed. In this work, we…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
This paper presents bilateral control laws for one-dimensional(1-D) linear 2x2 hyperbolic first-order systems (with spatially varying coefficients). Bilateral control means there are two actuators at each end of the domain. This situation…
In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…
For the classes of finite dimensional linear time-invariant semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations, stability and hypocoercivity are discussed and related to concepts from control…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
We introduce a scheme for controlling physical and other quantities; utilizing noise-based logic for control-and-optimization with high dimensionality, similarly how the Hilbert space of quantum informatics can be utilized for such purpose.…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
This work considers the Galerkin approximation and analysis for a hyperbolic integrodifferential equation, where the non-positive variable-sign kernel and nonlinear-nonlocal damping with both the weak and viscous damping effects are…
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 paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…
We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact…
The hyperspherical adiabatic expansion method is used to describe correlations in a symmetric boson system rigorously confined to two spatial dimensions. The hyperangular eigenvalue equation turns out to be almost independent of the…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…