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

Carlo Bianca and Christian Dogbe ()
Additional contact information
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

Mathematics, 2025, vol. 13, issue 5, 1-18

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.

Keywords: nonlinear PDEs; PDEs in infinite-dimensional Hilbert space; Hamilton–Jacobi equations; stationary equation; viscosity solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/5/703/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/5/703/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:5:p:703-:d:1596843

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().