2025/04/22 by Evgeny Yu. Panov, Panov, Evgeny Yu.
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fixed Point Theorems Analysis #Fuzzy Systems and Optimization #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2504.16232
openalex publication_date 2025/04/22 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest a criteria of uniqueness of this semigroup. We also find a stronger criteria of uniqueness of generalized solutions. Applications to transport equations with solenoidal (and generally discontinuous) coefficients are given.