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Stabilization for a degenerate wave equation with time-varying delay in the boundary control input

Menglan Liao

Abstract

A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is concerned and the uniform exponential decay of solutions is obtained by combining the energy estimates with suitable Lyapunov functionals and an integral inequality under suitable conditions.

Stabilization for a degenerate wave equation with time-varying delay in the boundary control input

Abstract

A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is concerned and the uniform exponential decay of solutions is obtained by combining the energy estimates with suitable Lyapunov functionals and an integral inequality under suitable conditions.

Paper Structure

This paper contains 4 sections, 13 theorems, 94 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Well-posedness
  4. Exponential stability

Key Result

Proposition 2.1

A2017 Let 1.2 hold. Then the following properties hold

Theorems & Definitions (20)

  • Proposition 2.1
  • Proposition 2.2
  • Proposition 2.3
  • Theorem 2.4
  • Theorem 3.1
  • Lemma 3.2
  • proof
  • Theorem 3.3
  • proof
  • Corollary 3.4
  • ...and 10 more