Related papers: Guaranteeing Spatial Uniformity in Diffusively-Cou…
A class of coupled cell-bulk ODE-PDE models is formulated and analyzed in a two-dimensional domain, which is relevant to studying quorum sensing behavior on thin substrates. In this model, spatially segregated dynamically active signaling…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
We derive explicit pointwise bounds for the spatial derivative $\left| \frac{\partial V}{\partial x} \right|$ of solutions to linear parabolic PDEs with Neumann boundary conditions. The bound is fully explicit in the sense that it depends…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…
In this paper, a high-order exponential scheme is developed to solve the 1D unsteady convection-diffusion equation with Neumann boundary conditions. The present method applies fourth-order compact exponential difference scheme in spatial…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…
In this work, we present a scalable Linear Matrix Inequality (LMI) based framework to verify the stability of a set of linear Partial Differential Equations (PDEs) in one spatial dimension coupled with a set of Ordinary Differential…
Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…
The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic…
We analyze oscillatory instabilities for a coupled PDE-ODE system modeling the communication between localized spatially segregated dynamically active signaling compartments that are coupled through a passive extracellular bulk diffusion…
The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps.…
Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by…
We study the well-posedness and asymptotic behaviour of selected PDE-PDE and PDE-ODE systems on one-dimensional spatial domains, namely a boundary coupled wave-heat system and a wave equation with a dynamic boundary condition. We prove…
This letter investigates the problem of output synchronisation in heterogeneous dynamical networks with nonlinear diffusive couplings in the presence of disturbances on the coupling links. By exploiting relative dissipativity properties…
In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…
It is classical that uniform stabilization of solutions to the autonomous damped wave equation is equivalent to every geodesic meeting the positive set of the damping, which is called the geometric control condition. In this paper, it is…
We consider a class of non-linear dynamics on a graph that contains and generalizes various models from network systems and control and study convergence to uniform agreement states using gradient methods. In particular, under the…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…