Related papers: Identifiability and Global Stability Analysis on S…
Partial Differential Equations (PDEs) play a crucial role as tools for modeling and comprehending intricate natural processes, notably within the domain of biology. This research explores the domain of microbial activity within the complex…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and…
Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by…
Many physical problems can be modelled by partial differential equations on unknown domains. Several examples can easily be found in the dynamics of free interfaces in fluid dynamics, solid mechanics or in fluid-solid interactions. To solve…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
Due to unbounded input operators in partial differential equations (PDEs) with boundary inputs, there has been a long-held intuition that input-to-state stability (ISS) properties and finite gains cannot be established with respect to…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Understanding sustainability through modeling involves one of the complex and interdisciplinary activities where mathematics plays a key role. We provide arguments favoring the need for developing global models for measuring the status of…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…
We present a series of recent results on the well-posedness of very singular parabolic stochastic partial differential equations. These equations are such that the question of what it even means to be a solution is highly non-trivial. This…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
Usually, the systems of partial differential equations (PDEs) are discovered from observational data in the single vector equation form. However, this approach restricts the application to the real cases, where, for example, the form of the…
In this work we study the problem about learning a partial differential equation (PDE) from its solution data. PDEs of various types are used as examples to illustrate how much the solution data can reveal the PDE operator depending on the…
In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…
We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…
Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the…
A direct method for the computation of polynomial conservation laws of polynomial systems of nonlinear partial differential equations (PDEs) in multi-dimensions is presented. The method avoids advanced differential-geometric tools. Instead,…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs…
In this article we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose…