Recursos de colección
Chan, Chi Hin; Vasseur, Alexis
Yang, Chuan-Fu; Yang, Jian-Xin
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.
Wei, Juncheng; Winter, Matthias
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...
Emamizadeh, B.; Mehrabi, M. H.
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.
Kim, Hyun-Chull; Ko, Mi-Hwa; Kim, Tae-Sung
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...
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.
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.
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.
Sghaier, M.; Alaya, J.
Hesaaraki, M.; Moradifam, A.
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.
Yamauchi, Yusuke
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.
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...
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...
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...