Related papers: On a class of PDEs with nonlinear distributed in s…
In this paper we consider a class of impulsive nonlinear differential equations with adaptive state-dependent delays. We discuss the existence and uniqueness of solutions of the initial value problem using a Picard-Lindel\"of type argument…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
We propose a new method for constructing exact solutions to nonlinear delay reaction--diffusion equations of the form $$ u_t=ku_{xx}+F(u,w), $$ where $u=u(x,t)$, $w=u(x,t-\tau)$, and $\tau$ is the delay time. The method is based on…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
In this paper, we establish a theory of well-posedness for delay differential equations (DDEs) via notions of \textit{prolongations} and \textit{$C^1$-prolongations}, which are continuous and continuously differentiable extensions of…
The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
The purpose of this paper is to introduce a semigroup approach to linear integro-differential systems with delays in state, control and observation parts. On the one hand, we use product spaces to reformulate state-delay…
In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
We extend a contraction mapping argument for ordinary state-dependent delay differential equations to evolutionary partial differential equations in the sense of R. Picard, that is, to equations of the form $\bigl(\partial_{t}…
We consider a nonlinear transmission problem for a Bresse beam, which consists of two parts, damped and undamped. The mechanical damping in the damped part is present in the shear angle equation only, and the damped part may be of arbitrary…
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated…