SIAM Journal on Mathematical Analysis http://scitation.aip.org/ SIAM Journal on Mathematical Analysis Nonlinear Stability of Periodic Traveling Wave Solutions of the Generalized Kortewegde Vries Equation http://link.aip.org/link/?SJM/41/1921/1&agg=rss Mathew A. Johnson<br/> In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Kortewegde Vries equation $u_t=u_{xxx}+f(u)_x$. In particular, we derive sufficient conditions for such a solution to be orbitally stable in terms of the Hess ... [SIAM J. Math. Anal. 41, 1921 (2009)] published Wed Nov 18, 2009. Localized Modes of the Linear Periodic Schrodinger Operator with a Nonlocal Perturbation http://link.aip.org/link/?SJM/41/1967/1&agg=rss Tomas Dohnal, Michael Plum, and Wolfgang Reichel<br/> We consider the existence of localized modes corresponding to eigenvalues of the periodic Schrodinger operator $-\partial_x^2+V(x)$ with an interface. The interface is modeled by a jump either in the value or the derivative of $V(x)$ and, in general, does not correspond to a localized perturbation ... [SIAM J. Math. Anal. 41, 1967 (2009)] published Wed Nov 18, 2009. Some New Well-Posedness Results for Continuity and Transport Equations, and Applications to the Chromatography System http://link.aip.org/link/?SJM/41/1890/1&agg=rss Luigi Ambrosio, Gianluca Crippa, Alessio Figalli, and Laura V. Spinolo<br/> We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly having a blow-up of the $BV$ norm at the initial time. We ... [SIAM J. Math. Anal. 41, 1890 (2009)] published Wed Nov 18, 2009. An Inverse Backscatter Problem for Electric Impedance Tomography http://link.aip.org/link/?SJM/41/1948/1&agg=rss Martin Hanke, Nuutti Hyvonen, and Stefanie Reusswig<br/> We consider a variant of (two dimensional) electric impedance tomography with very sparse data that resemble so-called backscatter data in inverse scattering. Such data arise in practice if the same single pair of electrodes is used to drive currents and measure voltage differences, subsequently at ... [SIAM J. Math. Anal. 41, 1948 (2009)] published Wed Nov 18, 2009. Homogenization of Fiber Reinforced Brittle Materials: The Extremal Cases http://link.aip.org/link/?SJM/41/1874/1&agg=rss Marco Barchiesi and Gianni Dal Maso<br/> We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\varepsilon$ of the grid and the ratio $\delta$ between the th ... [SIAM J. Math. Anal. 41, 1874 (2009)] published Wed Nov 18, 2009. A Bottle in a Freezer http://link.aip.org/link/?SJM/41/1851/1&agg=rss Pavel KrejCi, Elisabetta Rocca, and Jurgen Sprekels<br/> We propose here a model for solidification of the liquid content of an elastic bottle in a freezer. The main goal is to explain the occurrence of high stresses inside the bottle. As a by-product, we derive a formula for the undercooling coefficient in terms of the elasticity constants, latent heat, ... [SIAM J. Math. Anal. 41, 1851 (2009)] published Wed Nov 11, 2009. Characterization and Regularity for Axisymmetric Solenoidal Vector Fields with Application to NavierStokes Equation http://link.aip.org/link/?SJM/41/1825/1&agg=rss Jian-Guo Liu and Wei-Cheng Wang<br/> We consider the vorticity-stream formulation of axisymmetric incompressible flows and its equivalence with the primitive formulation. It is shown that, to characterize the regularity of a divergence free axisymmetric vector field in terms of the swirling components, an extra set of pole conditions ... [SIAM J. Math. Anal. 41, 1825 (2009)] published Wed Nov 11, 2009. Global Uniqueness of Transonic Shocks in Divergent Nozzles for Steady Potential Flows http://link.aip.org/link/?SJM/41/1816/1&agg=rss Li Liu and Hairong Yuan<br/> We show that for steady compressible potential flow in a class of straight divergent nozzles with arbitrary cross-section, if the flow is supersonic and spherically symmetric at the entry and the given pressure (resp., velocity) is appropriately large (resp., small) and also spherically symmetric a ... [SIAM J. Math. Anal. 41, 1816 (2009)] published Thu Nov 5, 2009. From Strong to Very Weak Solutions to the Stokes System with Navier Boundary Conditions in the Half-Space http://link.aip.org/link/?SJM/41/1792/1&agg=rss Cherif Amrouche, Sarka NeCasova, and Yves Raudin<br/> We consider the Stokes problem with slip-type boundary conditions in the half-space $\mathbb{R}^n_+$, with $n\geqslant2$. The weighted Sobolev spaces yield the functional framework. We first study generalized and strong solutions and then the case with very low regularity of data on the boundary. W ... [SIAM J. Math. Anal. 41, 1792 (2009)] published Thu Nov 5, 2009. Convergence Rate Toward Planar Stationary Waves for Compressible Viscous Fluid in Multidimensional Half Space http://link.aip.org/link/?SJM/41/1757/1&agg=rss Tohru Nakamura and Shinya Nishibata<br/> The present paper concerns a large-time behavior of motion of isentropic and compressible viscous fluid in a two- or three-dimensional half space. We obtain a convergence rate of a solution toward a planar stationary wave for an outflow problem, where fluid flows out through a boundary. For a super ... [SIAM J. Math. Anal. 41, 1757 (2009)] published Thu Oct 29, 2009.