Approximation of Degenerate Hyperbolic Equations with Interior Degeneracy and Applications to Controllability

TL;DR

This paper develops an approximation method for degenerate hyperbolic equations with interior degeneracy and applies it to establish controllability results, pioneering in higher dimensions.

Contribution

It introduces a novel approximation approach for degenerate hyperbolic equations and explores their controllability, filling a gap in higher-dimensional cases.

Findings

Established existence of solutions for degenerate hyperbolic equations.

Developed an approximation scheme using uniformly hyperbolic equations.

Derived controllability results for the original degenerate equations.

Abstract

In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably, this specific approximation result has remained unexplored in the existing body of literature. Ultimately, we utilize this approximation framework to derive controllability results for the original degenerate hyperbolic equations, marking what could potentially be the inaugural investigation into higher-dimensional degenerate hyperbolic equations.