19 papers · ranked by Valyu relevance
Declan S. Jagt, Matthew M. Peet
— Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain a PIE representation of any suitably well-posed 1D PDE model with constant…
Andrei D. Polyanin
nonlinear PDEs and delay PDEs Authors: ['Andrei D. Polyanin'] Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related equations. It is…
Andrei D. Polyanin, Alexei I. Zhurov
where u = u(x, t), w = u(x, t−τ), and τ is the delay time. The method is based on searching for solutions in the form u = PN n=1 ξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or functional equations) and the original delay partial…
Christopher N. Angstmann, Stuart-James M. Burney, Daniel Han, B. I. Henry + 1 more
'B. I. Henry' 'Zhijie Xu'] Exact solutions are derived for a time-delay advection equation and a fractional-order time-delay advection equation with a time-delay in the spatial derivative. Solutions are obtained, for arbitrary separable initial conditions, by incorporating recently introduced delay functions in a…
Dongfang Li, Chengjian Zhang
For a consistent numerical method to be practically useful, it is widely accepted that it must preserve the asymptotic stability of the original continuous problem. However, in this study, we show that it may lead to unreliable numerical solutions in long time simulation even if a classical numerical method gives a…
Ji Wang, Mamadou Diagne
—This paper presents a delay-adaptive boundary control scheme for a 2×2 coupled linear hyperbolic PDE-ODE cascade system with an unknown and arbitrarily long input delay. To construct a nominal delay-compensated control law, assuming a known input delay, a three-step backstepping design is used. Based on the certainty…
Joseph G. Conlon, Michael Dabkowski
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov function. It is shown that stability for the PDE is equivalent to stability for a…
Ababi Hailu Ejere, Tekle Gemechu Dinka, Mesfin Mekuria Woldaregay, Gemechis File Duressa
'Gemechis File Duressa'] Objective The paper is focused on developing and analyzing a uniformly convergent numerical scheme for a singularly perturbed reaction-diffusion problem with a negative shift. The solution of such problem exhibits strong boundary layers at the two ends of the domain due to the influence of the…
Souma Jinno, Shuji Kitora, Hiroshi Toki, Masayuki Abe
We formulate a numerical method on the transmission and radiation theory of three-dimensional conductors starting from the Maxwell equations in the time domain. We include the delay effect in the integral equations for the scalar and vector potentials rigorously, which is vital to obtain numerically stable solutions…
Brahim Benhammouda, Hector Vazquez-Leal
This work presents an analytical solution of some nonlinear delay differential equations (DDEs) with variable delays. Such DDEs are difficult to treat numerically and cannot be solved by existing general purpose codes. A new method of steps combined with the differential transform method (DTM) is proposed as a powerful…
Rohul Amin, Shah Nazir, Iván García-Magariño
Wireless sensor network and industrial internet of things have been a growing area of research which is exploited in various fields such as smart home, smart industries, smart transportation, and so on. There is a need of a mechanism which can easily tackle the problems of nonlinear delay integro-differential equations…
Abdelmalik Moujahid, Fernando Vadillo
Time delays are a fundamental feature in modeling stochastic epidemic systems, as they capture the incubation period and other physiological lags inherent in disease transmission. In this work, we investigate a stochastic SIRC (Susceptible-Infectious-Recovered-Cross-immune) epidemic model where the delay is…
Matthew J Simpson, Ryan J Murphy, Oliver J Maclaren
Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations of biological cells. Count data, by definition, is non-negative, and count data relating to biological populations is…
Pushpendra Kumar, Dumitru Baleanu, Vedat Suat Erturk, Mustafa Inc + 1 more
'V. Govindaraj'] We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point…
Guy Avraham, Raz Leib, Assaf Pressman, Lucia S. Simo + 4 more
To accurately estimate the state of the body, the nervous system needs to account for delays between signals from different sensory modalities. To investigate how such delays may be represented in the sensorimotor system, we asked human participants to play a virtual pong game in which the movement of the virtual…
Reiko Shintaki, Daiki Tanaka, Moe Okayasu, Shinsuke Suzuki + 4 more
Our preference for a reward depends on the time of delay for its delivery. Here we show that changes in the external environment can manipulate the perceived duration of time, which alters the formation of the choice preference through value signals in the cortical and subcortical brain regions. Humans anticipated a…
Sadegh Marzban, Renji Han, Nóra Juhász, Gergely Röst
We propose a hybrid partial differential equation – agent-based (PDE–ABM) model to describe the spatio-temporal viral dynamics in a cell population. The virus concentration is considered as a continuous variable and virus movement is modelled by diffusion, while changes in the states of cells (i.e. healthy, infected…
Shengjie Xu, Jeffrey C. Erlich, Evgeniya Lukinova
This preregistered fMRI study investigates the neural mechanisms underlying intertemporal choices involving waiting and postponing. On a behavioral level, choices made regarding rewards available in seconds that require waiting compared to choices about rewards postponed to a number days are surprisingly similar. The…
Sayed Naseel Mohamed Thangal, J. Maxwell Donelan
As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose motion, delaying the completion of the movement—we refer to this additional elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker…