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<p>We study the wellposedness and stabilization for a 2D coupled wave equations with nonlinearities of arbitrary growth and locally distributed nonlinear dissipation posed in a bounded domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. We give a proof based on the truncation of the original problem and passage to the limit in order to obtain in one shot, the energy identity as well as the observability inequality, which are the essential ingredients to obtain uniform decay rates of the energy. One advantage of our proof is that the decay rate is independent of the nonlinearity.</p>

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Decay Estimates for Coupled Semilinear Wave Systems with Exponential Sources and Locally Distributed Damping

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • José Guilherme Simion Antunes,
  • Adriana Flores de Almeida

摘要

We study the wellposedness and stabilization for a 2D coupled wave equations with nonlinearities of arbitrary growth and locally distributed nonlinear dissipation posed in a bounded domain \(\Omega \) Ω of \(\mathbb {R}^2\) R 2 . We give a proof based on the truncation of the original problem and passage to the limit in order to obtain in one shot, the energy identity as well as the observability inequality, which are the essential ingredients to obtain uniform decay rates of the energy. One advantage of our proof is that the decay rate is independent of the nonlinearity.