2023/05/18 by Soham Gokhale, Gokhale, Soham, Utpal Manna +1 · 1 citation
Economics, Econometrics and Finance · #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2305.10861
openalex publication_date 2023/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the stochastic Landau-Lifshitz-Bloch equation in dimensions 1,2,3, perturbed by a real-valued Wiener process. We consider a Suslin space-valued control process with a general control operator, which can depend on both the control and the corresponding solution. We reduce the equation to a more general (relaxed) form, where the concept of Young measures is used. We then show the existence of a weak martingale solution to the controlled equation (relaxed). In the second part of the work, we show that for a general lower semicontinuous cost functional, the problem admits a weak relaxed optimal control. This is done using the theory of Young measures. Moreover, pathwise uniqueness is shown (for dimensions 1,2), which implies the existence of a strong solution.