Related papers: Parameter identification for an uncertain reaction…
We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions in domains with a particular geometry (annular type domains). We establish Lipschitz stability estimates in L^2…
This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…
In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation and Brownian diffusion. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to…
Distributional regression aims at estimating the conditional distribution of a targetvariable given explanatory co-variates. It is a crucial tool for forecasting whena precise uncertainty quantification is required. A popular methodology…
This paper presents boundary observer design for space and time dependent reaction-advection-diffusion equations using backstepping method. The method uses only a single measurement at the boundary of the systems. The existence of the…
Reactive sputtering is a plasma-based technique to deposit a thin film on a substrate. This contribution presents a novel parameter-interval estimation method for a well-established model that describes the uncertain and nonlinear reactive…
A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The problem is discretized using $P_1$ finite elements in space,…
Estimators of parameters of truncated distributions, namely the truncated normal distribution, have been widely studied for a known truncation region. There is also literature for estimating the unknown bounds for known parent…
The concentration of radiation-induced point defects in general materials under irradiation is commonly described by the point defect kinetics equations based on rate theory. However, the parametric uncertainty in describing the rate…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
We focus on the control of unknown Partial Differential Equations (PDEs). The system dynamics is unknown, but we assume we are able to observe its evolution for a given control input, as typical in a Reinforcement Learning framework. We…
A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have…
In a scalar reaction-diffusion equation, it is known that the stability of a steady state can be determined from the Maslov index, a topological invariant that counts the state's critical points. In particular, this implies that pulse…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport…
We study the problem of parameter estimation for large exchangeable interacting particle systems when a sample of discrete observations from a single particle is known. We propose a novel method based on martingale estimating functions…
We concider, the blow-up solutions for a coupled reaction diffusion system with gradient terms. The main purpose is to understand whether the gradient terms effect the blow-up properties. We derive the upper and lower blow-up rate estimates…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
The rate coefficient formulae of unimolecular reactions are generalized to the systems with the power-law distributions based on nonextensive statistics, and the power-law rate coefficients are derived in the high and low pressure limits,…