Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

Amphiphilic thermoset elastomers from metal‐free,click crosslinking of PEG‐grafted silicone surfactants

The hydrophobicity of silicone elastomers can compromise their utility in some biomaterials applications. Few effective processes exist to introduce hydrophilic groups onto a polysiloxane backbone and subsequently crosslink the material into elastomers. This problem can be overcome through the utilization of metal‐free click reactions between azidoalkylsilicones and alkynyl‐modified silicones and/or PEGs to both functionalize and crosslink silicone elastomers. Alkynyl‐functional PEG was clicked onto a fraction of the available azido groups of a functional polysiloxane, yielding azido reactive PDMS‐g‐PEG rake surfactants. The reactive polymers were then used to crosslink alkynyl‐terminated PDMS of different molecular weights. Using simple starting materials, this generic yet versatile method permits the preparation and characterization of a library of amphiphilic thermoset elastomers that vary in their composition, crosslink density, elasticity, hydrogel formation, and wettability. An appropriate balance of PEG length and crosslink density leads to a permanently highly wettable silicone elastomer that demonstrated very low levels of protein adsorption. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1082–1093     

Stability of Semiconductor States with Insulating and Contact Boundary Conditions

We prove the existence of global smooth solutions near a given steady state of the hydrodynamic model of the semiconductors in a bounded domain with physical boundary conditions. The steady state and the doping profile are permitted to be of large variation but the initial velocity must be small. Two cases are considered. In the first one the problem is three-dimensional, the boundary conditions are insulating and the steady state velocity vanishes. In the second one, the problem is one-dimensional, the boundary is of contact type and the steady state velocity does not vanish.     

Diffeomorphism finiteness for manifolds with ricci curvature andL n/2-norm of curvature bounded

Partially supported by NSF Grants.