Divergence boundary conditions for vector Helmholtz equations with divergence constraints
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Divergence forms of the infinity-Laplacian.
The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv
Divergence stability in connection with the -version of the finite element method
Divergent solutions to the 5D Hartree equations
We consider the Cauchy problem for the focusing Hartree equation in ℝ⁵ with initial data in H¹, and study the divergence property of infinite-variance and nonradial solutions. For the ground state solution of in ℝ⁵, we prove that if u₀ ∈ H¹ satisfies M(u₀)E(u₀) < M(Q)E(Q) and ||∇u₀||₂||u₀||₂ > ||∇Q||₂||Q||₂, then the corresponding solution u(t) either blows up in finite forward time, or exists globally for positive time and there exists a time sequence tₙ → ∞ such that ||∇u(tₙ)||₂ → ∞....
Division Problem and Partial Differential Equations with Constant Coefficients in Colombeau's Space of New Generalized Functions.
Do all integrable evolution equations have the Painlevé property?
Do Demographic and Disease Structures Affect the Recurrence of Epidemics ?
In this paper we present an epidemic model affecting an age-structured population. We show by numerical simulations that this demographic structure can induce persistent oscillations in the epidemic. The model is then extended to encompass a stage-structured disease within an age-dependent population. In this case as well, persistent oscillations are observed in the infected as well as in the whole population.
Do global attractors depend on boundary conditions?
Does Atkinson-Wilcox Expansion Converges for any Convex Domain?
2000 Mathematics Subject Classification: 35C10, 35C20, 35P25, 47A40, 58D30, 81U40.The Atkinson-Wilcox theorem claims that any scattered field in the exterior of a sphere can be expanded into a uniformly and absolutely convergent series in inverse powers of the radial variable and that once the leading coefficient of the expansion is known the full series can be recovered uniquely through a recurrence relation. The leading coefficient of the series is known as the scattering amplitude or the far...
Domain decomposition algorithms for first-order system least squares methods.
Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes.
Domain geometry and the Pohozaev identity.
Domain identification for semilinear elliptic equations in the plane: The zero flux case.
Domain optimization in -axisymmetric elliptic problems by dual finite element method
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. The shape of the domain has to be found so as to minimize a cost functional, which is given in terms of the cogradient of the solution. A new dual finite element method is used for approximate solutions. The existence of an optimal domain is proven and a convergence analysis presented.
Domain optimization in axisymmetric elliptic boundary value problems by finite elements
An axisymmetric second order elliptic problem with mixed boundary conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The existence of an optimal boundary is proven and a convergence analysis for piecewise linear approximate solutions presented, using weighted Sobolev spaces.
Domain optimization in axisymmetric elliptic problems
Domain perturbation method and local minimizers to Ginzburg-Landau functional with magnetic effect.
Domain perturbations, capacity and shift of eigenvalues
After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator . If is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in Capacity in abstract Hilbert spaces and applications to higher order differential operators (Comm. P. D. E., 24:759–775,...
Domain sensitivity in singular limits of compressible viscous fluids
In this note, we discuss several recently developed methods for studying stability of a singular limit process with respect to the shape of the underlying physical space. As a model example, we consider a compressible viscous barotropic fluid occupying a spatial domain . In what follows, we describe two rather different problems: (i) the choice of effective boundary conditions; (ii) the fluid flow in the low Mach number regime. In the remaining part of the paper, we analyze these two issues simultaneously...