Related papers: Stabilizing Radial Basis Function Methods for Cons…
An optimally efficient explicit numerical scheme for solving fluid dynamics equations, or any other parabolic or hyperbolic system of partial differential equations, should allow local regions to advance in time with their own, locally…
This paper addresses the three concepts of \textit{ consistency, stability and convergence } in the context of compact finite volume schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of…
We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to construct basis functions that are local in parameter and time…
Aim of these notes is provide a brief review of the current well-posedness theory for hyperbolic systems of conservation laws in one space dimension, also pointing out open problems and possible research directions. They supplement the…
Control barrier functions (CBFs) have been demonstrated as an effective method for safety-critical control of autonomous systems. Although CBFs are simple to deploy, their design remains challenging, motivating the development of…
This work was motivated by a lacking general consensus in the exact form of the boundary conditions (BCs) required on the solid surfaces for the continuum modeling of RF plasmas. Various kinds of number and energy density BCs on solid…
Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) can be combined, typically by means of Quadratic Programs (QPs), to design controllers that achieve performance and safety objectives. However, a significant limitation…
We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide…
A hyperbolic group acts by homeomorphisms on its Gromov boundary. We use a dynamical coding of boundary points to show that such actions are topologically stable in the dynamical sense: any nearby action is semi-conjugate to (and an…
The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global…
Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations (PDEs) because they are flexible with respect to the geometry of the computational domain, they can…
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…
It has been recently observed that a scalar field with Robin boundary conditions (RBCs) can trigger both a superradiant and a bulk instability for a BTZ black hole (BH). To understand the generality and scrutinize the origin of this…
We present a new approach to analyze the validation of weakly nonlinear geometric optics for entropy solutions of nonlinear hyperbolic systems of conservation laws whose eigenvalues are allowed to have constant multiplicity and…
Model information can be used to predict future trajectories, so it has huge potential to avoid dangerous region when implementing reinforcement learning (RL) on real-world tasks, like autonomous driving. However, existing studies mostly…
An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…
In this paper, we study the stabilization problem for a hyperbolic type Stokes system posed on a bounded domain. We show that when the damping effects are restricted to a subdomain satisfying the geometrical control condition the system…
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…
We revisit a well-established model for highly re-entrant semi-conductor manufacturing systems, and analyze it in the setting of states, in- and outfluxes being Borel measures. This is motivated by the lack of optimal solutions in the…
We study the stability of one-dimensional linear lattice Boltzmann schemes for scalar hyperbolic equations with respect to boundary data. Our approach is based on the original raw algorithm on several unknowns, thereby avoiding the need for…