Related papers: Controlling the Growth of Constraints in Hyperboli…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
This work presents the existence and uniqueness of solution to a free boundary value problem related to biofilm growth. The problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species…
With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
In this article, we present a numerical approach to ensure the preservation of physical bounds on the solutions to linear and nonlinear hyperbolic convection-reaction problems at the discrete level. We provide a rigorous framework for error…
We study the evolution in equilibrium of the fluctuations for the conserved quantities of a chain of anharmonic oscillators in the hyperbolic space-time scaling. Boundary conditions are determined by applying a constant tension at one side,…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
Optimization algorithms are increasingly being used in applications with limited time budgets. In many real-time and embedded scenarios, only a few iterations can be performed and traditional convergence metrics cannot be used to evaluate…
This paper tackles the problem of nonlinear systems, with sublinear growth but unbounded control, under perturbation of some time-varying state constraints. It is shown that, given a trajectory to be approximated, one can find a neighboring…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…
Physical fundamentals of the self-organizing theory for the system with varying constraints are considered. A variation principle, specifically the principle of dynamic harmonization as a generalization of the Gauss-Hertz principle for the…
For robots to handle the numerous factors that can affect them in the real world, they must adapt to changes and unexpected events. Evolutionary robotics tries to solve some of these issues by automatically optimizing a robot for a specific…
Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct…
We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls…
In this paper we prove necessary conditions for optimality of a stochastic control problem for a class of stochastic partial differential equations that is controlled through the boundary. This kind of problems can be interpreted as a…
In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of…
Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the curl or the divergence of a vector that appear as an implicit constraint. In this article, we…
We establish a link between stability estimates for a hyperbolic inverse problem via the Boundary Control method and the blowup of a constant appearing in the contexts of optimal unique continuation and cost of approximate controllability.
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
Maxwell's equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell's equations into evolution equations and constraints, we derive the characteristic equation and we…