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<p>In this manuscript, we investigate the optimal control problem for a coupled semilinear system characterized by two wave equations in which the nonlinear function satisfies Lipschitz condition. The study begins by establishing the existence and uniqueness of the mild solution through the application of contraction mapping theorem in conjunction with a priori estimate technique. Following this, we prove the existence of an optimal pair for the integral convex cost problem and explore the problem of time optimal control. Finally, an illustrative example is provided to demonstrate the practical implications of our theoretical findings.</p>

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Existence of solution and optimal control results in coupled wave system with Lipschitz nonlinearity

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Sandeep Kumar,
  • Tajinder

摘要

In this manuscript, we investigate the optimal control problem for a coupled semilinear system characterized by two wave equations in which the nonlinear function satisfies Lipschitz condition. The study begins by establishing the existence and uniqueness of the mild solution through the application of contraction mapping theorem in conjunction with a priori estimate technique. Following this, we prove the existence of an optimal pair for the integral convex cost problem and explore the problem of time optimal control. Finally, an illustrative example is provided to demonstrate the practical implications of our theoretical findings.