Analysis of the Cahn–Hilliard Equation with a Relaxation Boundary Condition Modeling the Contact Angle Dynamics

We analyze the Cahn–Hilliard equation with a relaxation boundary condition modeling the evolution of an interface in contact with the solid boundary. An L ^∞ estimate is established which enables us to prove the global existence of the solution. We also study the sharp interface limit of the system. The dynamic of the contact point and the contact angle are derived and the results are compared with the numerical simulations.     

Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System

We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes system for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is proved that for the one-dimensional compressible Navier–Stokes system, the combination wave of a “viscous contact wave”, which corresponds to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave is suitably small. This result is proved by using elementary energy methods.     

Book Review ＂Fabrikant, V. I. Contact and Crack Problems in Linear Theory of Elasticity, Bentham Science Publishers, Sharjah, UAE （2010）＂

As suggested by the title, this extensive book is concerned with crack and contact problems in linear elasticity. However, in general, it is intended for a wide audience ranging from engineers to mathematical physicists. Indeed, numerous problems of both academic and technological interest in electro-magnetics,