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Unfoldings of foliations with multiform first integrals

Tatsuo Suwa (1983)

Annales de l'institut Fourier

Let F = ( ω ) be a codim 1 local foliation generated by a germ ω of the form ω = f 1 ... f p ∑ i = 1 p λ i d f i f i for some complex numbers λ i and germs f i of holomorphic functions at the origin in C n . We determine, under some conditions, the set of equivalence classes of first order unfoldings and construct explicitly a universal unfolding of F . Special cases of this include foliations with holomorphic or meromorphic first integrals. We also show that the unfolding theory for F is equivalent to the unfolding theory for the multiform function...

Uniform controllability for the beam equation with vanishing structural damping

Ioan Florin Bugariu (2014)

Czechoslovak Mathematical Journal

This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter ε ∈ ( 0 , 1 ) . We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls v ε as ε goes to zero. It is shown that for any time T sufficiently large but independent of ε and for each initial data in a suitable space there exists a uniformly bounded...

Uniform estimates for the parabolic Ginzburg–Landau equation

F. Bethuel, G. Orlandi (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider complex-valued solutions u ε of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of ℝ N , N ≥ 2 , where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy E ε ( u ε ) verifies the bound (natural in the context) E ε ( u ε ) ≤ M 0 | log ε | , where M 0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of u ε , as ε → 0 , is to establish uniform L p bounds for the gradient, for some p > 1 . We review some recent techniques developed in...

Uniform estimates for the parabolic Ginzburg–Landau equation

F. Bethuel, G. Orlandi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider complex-valued solutions uE of the Ginzburg–Landau equation on a smooth bounded simply connected domain Ω of ℝ N , N ≥ 2, where ε > 0 is a small parameter. We assume that the Ginzburg–Landau energy E ε ( u ε ) verifies the bound (natural in the context) E ε ( u ε ) ≤ M 0 | log ε | , where M0 is some given constant. We also make several assumptions on the boundary data. An important step in the asymptotic analysis of uE, as ε → 0, is to establish uniform Lp bounds for the gradient, for some p>1. We review some...

Uniqueness results for operators in the variational sequence

W. M. Mikulski (2009)

Annales Polonici Mathematici

We prove that the most interesting operators in the Euler-Lagrange complex from the variational bicomplex in infinite order jet spaces are determined up to multiplicative constant by the naturality requirement, provided the fibres of fibred manifolds have sufficiently large dimension. This result clarifies several important phenomena of the variational calculus on fibred manifolds.

Unitons and their moduli.

Anand, Christopher Kumar (1996)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Currently displaying 61 – 80 of 94