SIAM Journal on Mathematical Analysis http://scitation.aip.org/ SIAM Journal on Mathematical Analysis Global Classical Solutions for the VlasovMaxwellFokkerPlanck System http://link.aip.org/link/?SJM/42/459/1&agg=rss Tong Yang and Hongjun Yu<br/> We consider a classical model in the kinetic theory for plasmathe VlasovMaxwellFokkerPlanck system. Global-in-time classical solutions near Maxwellian are constructed based on an approach by combining the compensating function and energy method. In addition, a convergence rate in time of the soluti ... [SIAM J. Math. Anal. 42, 459 (2010)] published Fri Mar 12, 2010. Thin-Film Limits for LandauLifshitzGilbert Equations http://link.aip.org/link/?SJM/42/519/1&agg=rss Christof Melcher<br/> We derive a damped wave-type limit for the LandauLifshitzGilbert equation in thin films starting from the full micromagnetic model. The result, previously encountered in [A. Capella, C. Melcher, and F. Otto, Nonlinearity, 20 (2007), pp. 25192537] in the context of reduced models for domain wall mot ... [SIAM J. Math. Anal. 42, 519 (2010)] published Fri Mar 12, 2010. Stability of the Slow Manifold in the Primitive Equations http://link.aip.org/link/?SJM/42/427/1&agg=rss R. Temam and D. Wirosoetisno<br/> We show that, with some regularity hypotheses, the solution of the forced-dissipative rotating primitive equations of the ocean loses most of its fast, inertia-gravity, component in the small Rossby number limit as $t\to\infty$. At leading order in the Rossby number, the solution approaches what is ... [SIAM J. Math. Anal. 42, 427 (2010)] published Fri Mar 12, 2010. Multiphase Weakly Nonlinear Geometric Optics for Schrodinger Equations http://link.aip.org/link/?SJM/42/489/1&agg=rss Remi Carles, Eric Dumas, and Christof Sparber<br/> We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but ... [SIAM J. Math. Anal. 42, 489 (2010)] published Fri Mar 12, 2010. Results on the Diffusion Equation with Rough Coefficients http://link.aip.org/link/?SJM/42/406/1&agg=rss Burak Aksoylu and Horst R. Beyer<br/> We study the behavior of the solutions of the stationary diffusion equation as a function of a possibly rough ($L^{\infty}$-) diffusivity. This includes the boundary behavior of the solution maps, associating to each diffusivity the solution corresponding to some fixed source function, when the dif ... [SIAM J. Math. Anal. 42, 406 (2010)] published Fri Mar 12, 2010. Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary http://link.aip.org/link/?SJM/42/377/1&agg=rss Yihong Du and Zhigui Lin<br/> In this paper we investigate a diffusive logistic model with a free boundary in one space dimension. We aim to use the dynamics of such a problem to describe the spreading of a new or invasive species, with the free boundary representing the expanding front. We prove a spreading-vanishing dichotomy ... [SIAM J. Math. Anal. 42, 377 (2010)] published Wed Mar 10, 2010. Asymptotic Properties of Entropy Solutions to Fractal Burgers Equation http://link.aip.org/link/?SJM/42/354/1&agg=rss Nathael Alibaud, Cyril Imbert, and Grzegorz Karch<br/> We study properties of solutions of the initial value problem for the nonlinear and nonlocal equation $u_t+(-\partial^2_x)^{\alpha/2}u+uu_x=0$ with $\alpha\in(0,1]$, supplemented with an initial datum approaching the constant states $u_\pm$ ($u_-<u_+$) as $x\to\pm\infty$, respectively. It was shown ... [SIAM J. Math. Anal. 42, 354 (2010)] published Wed Mar 10, 2010. Convergence in Strongly Monotone Systems with an Increasing First Integral http://link.aip.org/link/?SJM/42/334/1&agg=rss Murad Banaji and David Angeli<br/> In this paper we generalize a useful result due to Mierczynski which states that for a strictly cooperative system on the positive orthant, with increasing first integral, all bounded orbits are convergent. Moreover there can be no more than one equilibrium on any level set, and any equilibrium att ... [SIAM J. Math. Anal. 42, 334 (2010)] published Wed Mar 10, 2010. On the Shortening Rate of Collections of Plane Convex Curves by the Area-Preserving Mean Curvature Flow http://link.aip.org/link/?SJM/42/323/1&agg=rss Shibin Dai<br/> Area-preserving mean curvature flows can be used to model some phase transitions. Geometrically, in the two-dimensional case, they describe the shortening of the curves that are interfaces separating the two phases while preserving the areas of each phase, respectively. Scaling arguments suggest th ... [SIAM J. Math. Anal. 42, 323 (2010)] published Fri Mar 5, 2010. On Universal Coercivity in Linear Elasticity http://link.aip.org/link/?SJM/42/298/1&agg=rss Kewei Zhang<br/> We consider a variational model for composition of finitely many strongly elliptic homogenous elastic materials in linear elasticity. We give conditions for universal coercivity for the variational integrals which are independent of particular compositions of materials involved. We show that in the ... [SIAM J. Math. Anal. 42, 298 (2010)] published Fri Mar 5, 2010.