On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow

In this article, we study the axisymmetric surface diffusion flow (ASD), a fourth-order geometric evolution law. In particular, we prove that ASD generates a real analytic semiflow in the space of (2 + \alpha)-little-H\"older regular surfaces of revolution embedded in R^3 and satisfying periodic boundary conditions. We also give conditions for global existence of solutions and prove that solutions are real analytic in time and space. Further, we investigate the geometric properties of solutions to ASD. Utilizing a connection to axisymmetric surfaces with constant mean curvature, we characterize the equilibria of ASD. Then, focusing on the family of cylinders, we establish results regarding stability, instability and bifurcation behavior, with the radius acting as a bifurcation parameter for the problem.Comment: 37 pages, 6 figures, To Appear in SIAM J. Math. Ana

Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence

We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation $$-\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq \mathbb{R}^{N},\ N\geq 3,$$ where $\Omega$ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\partial \Omega$ if $\Omega \neq \mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty$ if $\Omega$ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq 0$ is also considered.Comment: 29 pages, 8 figure

Lifespan theorem for constrained surface diffusion flows

We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists, and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of the concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.Comment: 29 pages. arXiv admin note: substantial text overlap with arXiv:1201.657

Functional diversity of chemokines and chemokine receptors in response to viral infection of the central nervous system.

Encounters with neurotropic viruses result in varied outcomes ranging from encephalitis, paralytic poliomyelitis or other serious consequences to relatively benign infection. One of the principal factors that control the outcome of infection is the localized tissue response and subsequent immune response directed against the invading toxic agent. It is the role of the immune system to contain and control the spread of virus infection in the central nervous system (CNS), and paradoxically, this response may also be pathologic. Chemokines are potent proinflammatory molecules whose expression within virally infected tissues is often associated with protection and/or pathology which correlates with migration and accumulation of immune cells. Indeed, studies with a neurotropic murine coronavirus, mouse hepatitis virus (MHV), have provided important insight into the functional roles of chemokines and chemokine receptors in participating in various aspects of host defense as well as disease development within the CNS. This chapter will highlight recent discoveries that have provided insight into the diverse biologic roles of chemokines and their receptors in coordinating immune responses following viral infection of the CNS

Chicken interferon-inducible transmembrane protein 3 restricts influenza viruses and lyssaviruses in vitro.

Interferon-inducible transmembrane protein 3 (IFITM3) is an effector protein of the innate immune system. It confers potent, cell-intrinsic resistance to infection by diverse enveloped viruses both in vitro and in vivo, including influenza viruses, West Nile virus, and dengue virus. IFITM3 prevents cytosolic entry of these viruses by blocking complete virus envelope fusion with cell endosome membranes. Although the IFITM locus, which includes IFITM1, -2, -3, and -5, is present in mammalian species, this locus has not been unambiguously identified or functionally characterized in avian species. Here, we show that the IFITM locus exists in chickens and is syntenic with the IFITM locus in mammals. The chicken IFITM3 protein restricts cell infection by influenza A viruses and lyssaviruses to a similar level as its human orthologue. Furthermore, we show that chicken IFITM3 is functional in chicken cells and that knockdown of constitutive expression in chicken fibroblasts results in enhanced infection by influenza A virus. Chicken IFITM2 and -3 are constitutively expressed in all tissues examined, whereas IFITM1 is only expressed in the bursa of Fabricius, gastrointestinal tract, cecal tonsil, and trachea. Despite being highly divergent at the amino acid level, IFITM3 proteins of birds and mammals can restrict replication of viruses that are able to infect different host species, suggesting IFITM proteins may provide a crucial barrier for zoonotic infections