Novel Rearrangements of 2,3-Dimercapto-1-propanol Derivatives: Formation of Dialkyl Sulfide, Dialkyl Disulfide, and 1,2,3-Tris(alkylthio)propane

The base alkylation of 2,3-dimercapto-1-propanol with alkyl halides leads in good yield to 2,3-bis(alkylthio)-1-propanol and dialkyl sulfide. The reaction of 2,3-bis(alkylthio)-1-propanol with catalytic concentrated sulfuric acid proceeds with rearrangement to give 1,2,3-tris(alkylthio)propane and dialkyl disulfide. The rearrangement reaction takes place through a common intermediate thiaranium intermediate 8.     

Non-linear parabolic problem associated with the penetration of a magnetic field into a substance

We study the following initial and boundary value problem: In section 1, with u₀ in L²(Ω), f continuous such that f(u) + ? non-decreasing for ? positive, we prove the existence of a unique solution on (0,T), for each T > 0. In section 2 it is proved that the unique soluition u belongs to L²(0, T; H ∩ H²) ∩ L^∞(0, T; H) if we assume u₀ in H and f in C¹(?,?). Numerical results are given for these two cases.