Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam

In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control actiondecays exponentially or in negative power of time t as t→∞.     

Entropy Production and Admissibility of Shocks

In shock wave theory there are two considerations in selecting the physically relevant shock waves.There is the admissibility criterion for the well-posedness of hyperbolic conservation laws.Another consideraztion concerns the entropy production across the shochs.The latter is natural from the physical point of view,but is not sufficient in its straightforward formulation,if the system is not genuinely nonlinear.In this paper we propose the principles of increasing entropy production and that of the superposition of shocks.These principles arc shown to be equivalent to the admissibility criterion.     

Recovery of An Unknown Flux in Parabolic Problems with Nonstandard Boundary Conditions: Error Estimates

In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain ^N, with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant (t), accompanied with a nonlocal (integral) Dirichlet side condition.We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution u and also of the unknown function .     

Galerkin Approximations for the Linear Parabolic Equation with the Third Boundary Condition

We solve a linear parabolic equation in ^d , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.     

Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines

In this paper we prove the equivalence between the existence of perfectly normal, non-metrizable, non-archimedean spaces and the existence of ``generalized Souslin lines", i.e., linearly ordered spaces in which every collection of disjoint open intervals is -discrete, but which do not have a -discrete dense set. The key ingredient is the observation that every first countable linearly ordered space has a dense non-archimedean subspace.

     

Higher Weierstrass points on

We study the arithmetic properties of higher Weierstrass points on modular curves for primes . In particular, for , we obtain a relationship between the reductions modulo of the collection of -Weierstrass points on and the supersingular locus in characteristic .

     

Dirichlet and Neumann boundary conditions: What is in between?

Given an admissible measure μ on where is an open set, we define a realization of the Laplacian in with general Robin boundary conditions and we show that generates a holomorphic C ₀ -semigroup on which is sandwiched by the Dirichlet Laplacian and the Neumann Laplacian semigroups. Moreover, under a locality and a regularity assumption, the generator of each sandwiched semigroup is of the form . We also show that if contains smooth functions, then μ is of the form (where σ is the (n-1)-dimensional Hausdorff measure and β a positive measurable bounded function on ); i.e. we have the classical Robin boundary conditions. RID="h1" ID="h1"Dédié à Philippe Bénilan RID="*" ID="h1"This work is part of the DGF-Project: "Regularit?t und Asymptotik für elliptische und parabolische Probleme".     

Boundary stabilization for a non‐linear beam on elastic bearings

In this paper, we study the equation under non‐linear boundary conditions which model the vibrations of a beam clamped at x=0 and supported by a non‐linear bearing at x=L. By adding only one damping mechanism at x=L, we prove the existence of a global solution and exponential decay of the energy. Copyright © 2001 John Wiley & Sons, Ltd.