Minimal time of the pointwise controllability for degenerate singular operators and related numerical results via B-splines

TL;DR

This paper investigates the minimal time for pointwise controllability of a degenerate/singular 1D equation, providing theoretical conditions and validating them through B-spline-based numerical simulations.

Contribution

It establishes controllability conditions for degenerate/singular equations and demonstrates their numerical approximation using B-splines.

Findings

Theoretical conditions for approximate and null controllability are proven.

Numerical simulations confirm the theoretical results.

B-spline based methods effectively approximate control and state functions.

Abstract

The goal of this paper is to analyze the pointwise controllability properties of a one-dimensional degenerate/singular equation. We prove the conditions that characterize approximate and null controllability. Besides, a numerical simulation based on B-splines will be provided, in which the state $u$ and the control function $h$ are represented in terms of B-spline basis functions. The numerical results obtained match the theoretical ones.