Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Flat SAR of P3-methylsulphonamide based small molecule legumain inhibitors

This letter describes the design, development and SAR exploration of a novel series of small legumain inhibitors. The SAR of a new small molecule legumain inhibitor chemotype was explored and found to have improved physiochemical properties compared to previously developed inhibitors within our group. However, further development of this series was found to be limited as the SAR was observed to be relatively flat.