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<p>In this article, we are interested in recovering a time-dependent source term from a sixth-order parabolic partial differential equation. The unknown time-dependent source term is recovered using an additional local integral measurement. First, we introduce a time-discrete scheme for the variational problem by using backward Euler’s method. Then, we prove this scheme’s existence and uniqueness results with the aid of Lax-Milgram lemma. Next, we prove some a priori estimates, which are inevitable to derive the main results of this article. Finally, using these a priori estimates, we derive the main results, which are the existence and uniqueness results for the inverse source problem.</p>

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Recovery of a time-dependent source term from a sixth-order parabolic partial differential equation

  • 期刊论文

  • 发表日期：

    2025年9月20日

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  • Navaneetha Krishnan Murugesan,
  • Barani Balan Natesan

摘要

In this article, we are interested in recovering a time-dependent source term from a sixth-order parabolic partial differential equation. The unknown time-dependent source term is recovered using an additional local integral measurement. First, we introduce a time-discrete scheme for the variational problem by using backward Euler’s method. Then, we prove this scheme’s existence and uniqueness results with the aid of Lax-Milgram lemma. Next, we prove some a priori estimates, which are inevitable to derive the main results of this article. Finally, using these a priori estimates, we derive the main results, which are the existence and uniqueness results for the inverse source problem.