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Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients
(2013-12-31)
In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension N ≥ 1. We will suppose the coefficients to be log-Zygmund continuous in time and ...
Random numbers from the tails of probability distributions using the transformation method
Fulger, D.; Scalas, E.
; Germano, G. (2013-12-31)
; Germano, G. (2013-12-31)
The speed of many one-line transformation methods for the production of, for example, Lévy alpha-stable random numbers, which generalize Gaussian ones, and Mittag-Leffler random numbers, which generalize exponential ones, ...
A regularity property for Schrödinger equations on bounded domains
(2013-12-31)
We give a regularity result for the free Schrödinger equations set in a bounded domain of ℝ N which extends the 1-dimensional result proved in Beauchard and Laurent (J. Math. Pures Appl. 94(5):520-554, 2010) with different ...
Optimal location of controllers for the one-dimensional wave equation
(2013-12-31)
In this paper, we consider the homogeneous one-dimensional wave equation defined on (0,π). For every subset ωâŠ[0,π] of positive measure, every T≥2π, and all initial data, there exists a unique control of minimal norm in ...
Derivation of a homogenized von-Kármán plate theory from 3D nonlinear elasticity
(2013-12-31)
We rigorously derive a homogenized von-Kármán plate theory as a Γ-limit from nonlinear three-dimensional elasticity by combining homogenization and dimension reduction. Our starting point is an energy functional that ...
Asymptotic expansions for anisotropic heat kernels
(2013-12-31)
We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lp-spaces. We mainly address two model examples. In the first one, the diffusivity ...
Explicit 2D ∞-harmonic maps whose interfaces have junctions and corners
(2013-12-31)
Given a map u:Ω⊆Rn→RN, the ∞-Laplacian is the system:(1)δ∞u:=(Du⊗Du+|Du|2[Du]⊥⊗I):D2u=0 and arises as the "Euler-Lagrange PDE" of the supremal functional E∞(u,Ω)={norm of matrix}Du{norm of matrix}L∞(Ω). (1) is the model ...
A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations
(2013-12-31)
We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different ...
A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators
(2013-12-31)
In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This ...
On an extension of a bilinear functional on Lp(Rd)⊗E to a Bochner space with an application to velocity averaging
(2013-12-31)
We examine necessary and sufficient conditions under which a continuous bilinear functional B on Lp(Rd)⊗E, p>1, E being a separable Banach space, can be continuously extended to a linear functional on Lp(Rd;E). The ...