<p>This paper investigates an inverse problem of determining the time-dependent source term in a nonlinear p-biharmonic pseudoparabolic equation, where the main goal is to recover an unknown right-hand side using additional integral measurements. To handle the nonlinear structure, the original model is rewritten in an equivalent form that includes a nonlinear nonlocal operator. The existence of a weak solution is shown using the Galerkin approximation together with compactness arguments and monotonicity methods. By relying on these monotonicity properties and compactness theorems, the uniqueness of the weak solution is also established. As an additional result, the paper proves also the classical solvability of the inverse source problem for the linear biharmonic pseudoparabolic equation. In this simpler setting, a classical solution can be obtained through a series expansion in the eigenfunctions of the Dirichlet Laplacian, while Weyl-type inequalities for the eigenvalues are used to describe the admissible class of data.</p>

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Inverse source problem for p-Harmonic pseudoparabolic equation

  • S. E. Aitzhanov,
  • K. H. Bayetov,
  • Mansur I. Ismailov

摘要

This paper investigates an inverse problem of determining the time-dependent source term in a nonlinear p-biharmonic pseudoparabolic equation, where the main goal is to recover an unknown right-hand side using additional integral measurements. To handle the nonlinear structure, the original model is rewritten in an equivalent form that includes a nonlinear nonlocal operator. The existence of a weak solution is shown using the Galerkin approximation together with compactness arguments and monotonicity methods. By relying on these monotonicity properties and compactness theorems, the uniqueness of the weak solution is also established. As an additional result, the paper proves also the classical solvability of the inverse source problem for the linear biharmonic pseudoparabolic equation. In this simpler setting, a classical solution can be obtained through a series expansion in the eigenfunctions of the Dirichlet Laplacian, while Weyl-type inequalities for the eigenvalues are used to describe the admissible class of data.