Work

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

Year: 2025

Type: article

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.

Source: Mathematics

DOI: 10.3390/math13050703

Authors: Carlo Bianca, Christian Dogbe

Institutions: Université Paris-Panthéon-Assas, Engineering School of Information and Digital Technologies, Centre National de la Recherche Scientifique, Normandie Université, Université de Caen Normandie

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4407841866

FWCI:

Cites: 46

Cited by:

Related to: 10