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<p>In this paper, we study the degenerate beam equation on (0,1) with local damping. This damping is effective in a subset <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>ω</mi> <mo>:</mo> <mo>=</mo> <mo stretchy="false">[</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo stretchy="false">]</mo> </math></EquationSource> <EquationSource Format="TEX">$\omega :=[x_{1},x_{2}]$</EquationSource> </InlineEquation> of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(0,1)$</EquationSource> </InlineEquation> and the damping coefficient may vanish in some subsets of <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(0,1)$</EquationSource> </InlineEquation>. As the first step, we prove the existence of a solution for the degenerate beam equation. Then, we derive the exponential stability result of the system.</p>

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Stability for Degenerate Beam Equation with Local Degenerate Damping

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Lanzhi Cao,
  • Shugen Chai

摘要

In this paper, we study the degenerate beam equation on (0,1) with local damping. This damping is effective in a subset ω : = [ x 1 , x 2 ] $\omega :=[x_{1},x_{2}]$ of ( 0 , 1 ) $(0,1)$ and the damping coefficient may vanish in some subsets of ( 0 , 1 ) $(0,1)$ . As the first step, we prove the existence of a solution for the degenerate beam equation. Then, we derive the exponential stability result of the system.