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<p>This study establishes the existence of solutions and the optimal control for a semilinear system of partial differential equations (PDEs) characterized by nonlinear interactions. The study commences by demonstrating the existence of mild solutions utilizing Schauder’s fixed point theorem. Additionally, the study demonstrates the existence of an optimal state-control pair for the integral cost functional, achieved without relying on the Lipschitz nonlinearity assumption or uniqueness of solutions. The main result is obtained through a two-stage construction of a minimizing sequence.</p>

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Existence of Solutions and Optimal Control for Semilinear PDE Systems with Nonlinear Interactions

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Sandeep Kumar,
  • Tajinder

摘要

This study establishes the existence of solutions and the optimal control for a semilinear system of partial differential equations (PDEs) characterized by nonlinear interactions. The study commences by demonstrating the existence of mild solutions utilizing Schauder’s fixed point theorem. Additionally, the study demonstrates the existence of an optimal state-control pair for the integral cost functional, achieved without relying on the Lipschitz nonlinearity assumption or uniqueness of solutions. The main result is obtained through a two-stage construction of a minimizing sequence.