Related papers: Parameterization method for state-dependent delay …
This chapter focuses on variable maturation delay or, more precisely, on the mathematical description of a size-structured population consuming an unstructured resource. When the resource concentration is a known function of time, we can…
The parameter identifiability problem for a dynamical system is to determine whether the parameters of the system can be found from data for the outputs of the system. Verifying whether the parameters are identifiable is a necessary first…
We present Lyapunov stability and asymptotic stability theorems for steady state solutions of general state-dependent delay differential equations (DDEs) using Lyapunov-Razumikhin methods. Our results apply to DDEs with multiple discrete…
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite…
In this paper we study, at different levels of generality, certain systems of delay differential equations (DDE). One focus and motivation is a system with state-dependent delay (SD-DDE) that has been formulated to describe the maturation…
Classically, solution theories for state-dependent delay equations are developed in spaces of continuous or continuously differentiable functions. The former can be technically challenging to apply in as much as suitably Lipschitz…
A simple non-autonomous scalar differential equation with delay, exponential decay, nonlinear negative feedback and a periodic multiplicative coefficient is considered. It is shown that stable slowly oscillating periodic solutions with the…
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
This paper is to investigate if the solution of a hybrid stochastic functional differential equation (SFDE) with infinite delay can be approximated by the solution of the corresponding hybrid SFDE with finite delay. A positive result is…
We consider a class of dissipative stochastic differential equations (SDE's) with time-periodic coefficients in finite dimension, and the response of time-asymptotic probability measures induced by such SDE's to sufficiently regular, small…
Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
In this paper, we consider numerical approximation to periodic measure of a time periodic stochastic differential equations (SDEs) under weakly dissipative condition. For this we first study the existence of the periodic measure $\rho_t$…
Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…
In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver…
This work proposes a new procedure for the stabilization of time-delay systems using Static Output Feedback (SOF) control. A previous convex optimization approach to SOF for Ordinary Differential Equations (ODEs) is extended to time-delay…
In 1994 we showed that very large classes of systems of nonlinear PDEs have solutions which can be assimilated with usual measurable functions on the Euclidean domains of definition of the respective equations. Recently, the regularity of…