## Recursos de colección

1. #### Log Improvement of the Prodi-Serrin Criteria for Navier-Stokes Equations

Chan, Chi Hin; Vasseur, Alexis

2. #### Large Eigenvalues and Traces of Sturm-Liouville Equations on Star-shaped Graphs

Yang, Chuan-Fu; Yang, Jian-Xin

3. #### On Refinable Sets

Dai, Xin-Rong; Wang, Yang
A refinable set is a compact set with positive Lebesgue measure whose characteristic function satisfies a refinement equation. Refinable sets are a generalization of self-affine tiles. But unlike the latter, the refinement equations defining refinable sets may have negative coefficients, and a refinable set may not tile. In this paper, we establish some fundamental properties of these sets.

4. #### Existence, Classification and Stability Analysis of Multiple-peaked Solutions for the Gierer-Meinhardt System in R1

Wei, Juncheng; Winter, Matthias

5. #### Mathematical Justification of a Shallow Water Model

Bresch, Didier; Noble, Pascal
The shallow water equations are widely used to model the flow of a thin layer of fluid submitted to gravity forces. They are usually formally derived from the full incompressible Navier-Stokes equations with free surface under the modeling hypothesis that the pressure is hydrostatic, the flow is laminar, gradually varied and the characteristic fluid height is small relative to the characteristics flow length. This paper deals with the mathematical justification of such asymptotic process assuming a non zero surface tension coefficient and some constraints on the data. We also discuss relation between lubrication models and shallow water systems with no...

7. #### Impulsive Intergo-differential Equations and Stability of Moving Invariant Manifolds

Stamov, Gani Tr.
This paper study the stability of moving invariant manifolds of nonlinear impulsive integro-differential equations. The obtain results are based on the method of piecewise continuous Lyapunov’s functions and the comparison principle.

8. #### Asymptotics for Multivariate Linear Process with Negatively Associated Random Vectors

Kim, Hyun-Chull; Ko, Mi-Hwa; Kim, Tae-Sung

9. #### Large-time Behavior of Solutions to an Initial-boundary Value Problem on the Half Line for Scalar Viscous Conservation Law

Hashimoto, Itsuko; Matsumura, Akitaka
We study the large-time behavior of the solution to an initial boundary value problem on the half line for scalar conservation law, where the data on the boundary and also at the far field are prescribed. In the case where the flux is convex and the corresponding Riemann problem for the hyperbolic part admits the transonic rarefaction wave (which means its characteristic speed changes the sign), it is known by the work of Liu-Matsumura-Nishihara (’98) that the solution tends toward a linear superposition of the stationary solution and the rarefaction wave of the hyperbolic part. In this paper, it is proved that even for a quite wide class...

10. #### Asymptotics for Polynomials Satisfying a Certain Twin Asymptotic Periodic Recurrence Relation: Unbounded Cases

de Andrade, E.X.L.; Kurokawa, F.A.; Ranga, A. Sri Ranga
Polynomials satisfying a certain twin asymptotic periodic recurrence relation are considered. It is assumed that the coefficients of the recurrence formula are unbounded but vary regularly and have different behaviour for even and odd indices. The asymptotic behaviour of the ratio of contiguous polynomials is analyzed.

11. #### Existence of Positive Solutions due to Non-local Interactions in a Class of Nonlinear Boundary Value Problems

Davidson, Fordyce A.; Dodds, Niall
We consider a class of non-local boundary value problems of the type used to model a variety of physical and biological processes, from Ohmic heating to population dynamics. Of particular relevance therefore is the existence of positive solutions. We are interested in the existence of such solutions that arise as a direct consequence of the non-local interactions in the problem. Conditions are therefore imposed that preclude the existence of a positive solution for the related local problem. Under these conditions, we prove that there exists a unique positive solution to the boundary value problem for all sufficiently strong non-local interactions and no positive solutions exists otherwise.

12. #### An Asymptotic Analysis of Linear Interfacial Motion

Wang, Jin
In this paper, we perform an asymptotic study on slightly viscous flows between two immiscible incompressible fluids. The motion is governed by linearized Navier-Stokes equations together with interfacial conditions. A second-order asymptotic expansion with respect to viscosity is obtained by using the method of multiple scales. In particular, viscous decay rate for the interfacial wave amplitude and viscous correction for the phase speed are explicitly identified.

13. #### Semiclassical Forms of Class s = 2: The Symmetric Case, when \Phi(0) = 0

Sghaier, M.; Alaya, J.

15. #### On Disk-like Self-affine Tiles Arising from Polyominoes

Gmainer, Johannes; Thuswaldner, Jörg M.
In this paper we study a class of plane self-affine lattice tiles that are defined using polyominoes. In particular, we characterize which of these tiles are homeomorphic to a closed disk. It turns out that their topological structure depends very sensitively on their defining parameters. ¶ In order to achieve our results we use an algorithm of Scheicher and the second author which allows to determine neighbors of tiles in a systematic way as well as a criterion of Bandt and Wang, with that we can check disk-likeness of a self-affine tile by analyzing the set of its neighbors.

16. #### Blow-up Results for a Reaction-Diffusion System

Yamauchi, Yusuke

17. #### 2D Density-dependent Leray Problem with a Discontinuous Density

Ammar Khodja, Farid; Santos, Marcelo M.
We consider the existence of a solution for the stationary Navier-Stokes equations describing an inhomogeneous incompressible fluid in a two dimensional unbounded Y-shaped domain. We show the existence of a weak solution such that the density and velocity of the fluid tend to densities and parallel flows, respectively, prescribed at some ‘ends’ of the domain. We allow prescribed densities at different ends to have distinct values. In fact, we obtain the density in the L$\infty$-space.

18. #### Fixed-point Iterative Sweeping Methods for Static Hamilton-Jacobi Equations

Zhang, Yong-Tao; Zhao, Hong-Kai; Chen, Shanqin
Fast sweeping methods utilize the Gauss-Seidel iterations and alternating sweeping strategy to achieve the fast convergence for computations of static Hamilton-Jacobi equations. They take advantage of the properties of hyperbolic PDEs and try to cover a family of characteristics of the corresponding Hamilton-Jacobi equation in a certain direction simultaneously in each sweeping order. The time-marching approach to steady state calculation is much slower than the fast sweeping methods due to the CFL condition constraint. But this kind of fixed-point iterations as time- marching methods have explicit form and do not involve inverse operation of nonlinear Hamiltonian. So it can solve general Hamilton-Jacobi equations using any monotone numerical Hamiltonian and high...

19. #### On the Well-posedness of a Mathematical Model for Lithium-Ion Battery Systems

Wu, Jinbiao; Xu, Jinchao; Zou, Henghui
In this paper, we shall establish the well-posedness of a mathematical model for a special class of electrochemical power device – lithium-ion battery. The underlying partial differential equations in the model involve a (mix and fully) coupled system of quasi-linear elliptic and parabolic equations. By exploring some special structure, we are able to adopt the well-known Nash-Moser- DeGiorgi boot strap to establish suitable a priori supremum estimates for the electric potentials. Using the supremum estimates, we apply the Leray-Schauder theory to establish the existence and uniqueness of a subsystem of elliptic equations that describe the electric potentials in the model. We then employ a Schauder fix point theorem to...

20. #### Regularization for Accurate Numerical Wave Propagation in Discontinuous Media

Tornberg, Anna-Karin; Engquist, Björn
Structured computational grids are the basis for highly efficient numerical approximations of wave propagation. When there are discontinuous material coefficients the accuracy is typically reduced and there may also be stability problems. In a sequence of recent papers Gustafsson et al. proved stability of the Yee scheme and a higher order difference approximation based on a similar staggered structure, for the wave equation with general coefficients. In this paper, the Yee discretization is improved from first to second order by modifying the material coefficients close to the material interface. This is proven in the $L^2$ norm. The modified higher order discretization yields a second order error component originating from...

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