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Uniqueness Results of Semilinear Parabolic Equations in Infinite-Dimensional Hilbert Spaces

Author

Listed:
  • Carlo Bianca

    (EFREI Research Lab, Université Paris-Panthéon-Assas, 30/32 Avenue de la République, 94800 Villejuif, France)

  • Christian Dogbe

    (UNICAEN, CNRS, LMNO, Normandie University, 14000 Caen, France)

Abstract

This paper is devoted to the uniqueness of solutions for a class of nonhomogeneous stationary partial differential equations related to Hamilton–Jacobi-type equations in infinite-dimensional Hilbert spaces. Specifically, the uniqueness of the viscosity solution is established by employing the inf/sup-convolution approach in a separable infinite-dimensional Hilbert space. The proof is based on the Faedo–Galerkin approximate method by assuming the existence of a Hilbert–Schmidt operator and by employing modulus continuity and Lipschitz arguments. The results are of interest regarding the stochastic optimal control problem.

Suggested Citation

  • Carlo Bianca & Christian Dogbe, 2025. "Uniqueness Results of Semilinear Parabolic Equations in Infinite-Dimensional Hilbert Spaces," Mathematics, MDPI, vol. 13(5), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:703-:d:1596843
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