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<p>This paper investigates a system of nonlinear coupled sine-Gordon equations with Neumann boundary conditions. By employing the Faedo-Galerkin method, we establish the existence and uniqueness of both weak and strong solutions. The analysis is supported by energy estimates and compactness arguments. Further, we show that the solutions continuously depend on initial data in appropriate Sobolev spaces. These results contribute to the theoretical understanding of nonlinear wave equations arising in various physical contexts, including Josephson junctions and other systems exhibiting nonlinear coupling and wave propagation dynamics.</p>

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Global existence of a nonlinear coupled sine-Gordon system with Neumann boundary conditions

  • 期刊论文

  • 发表日期：

    2025年8月5日

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  • Ghassan A. Al-Juaifri,
  • Mohammed Homod Hashim,
  • Huda A. Challoob,
  • Akil J. Harfash

摘要

This paper investigates a system of nonlinear coupled sine-Gordon equations with Neumann boundary conditions. By employing the Faedo-Galerkin method, we establish the existence and uniqueness of both weak and strong solutions. The analysis is supported by energy estimates and compactness arguments. Further, we show that the solutions continuously depend on initial data in appropriate Sobolev spaces. These results contribute to the theoretical understanding of nonlinear wave equations arising in various physical contexts, including Josephson junctions and other systems exhibiting nonlinear coupling and wave propagation dynamics.