Ferruccio Colombini

Publications (6)0 Total impact

• Source

  Available from: ArXiv

  Article: Incoming and disappearing solutions for Maxwell's equations

  Ferruccio Colombini, Vesselin Petkov, Jeffrey Rauch
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  ABSTRACT: We prove that in contrast to the free wave equation in $\R^3$ there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming waves. With their aid, we construct dissipative boundary conditions and solutions to Maxwell's equations in the exterior of a sphere which decay exponentially as $t \to +\infty$. They are asymptotically disappearing. Disappearing solutions which are identically zero for $t \geq T > 0$ are constructed which satisfy maximal dissipative boundary conditions which depend on time $t$. Both types are invisible in scattering theory.
  09/2010;
• Article: Smooth localized parametric resonance for wave equations

  Ferruccio Colombini, Jeffrey Rauch
  Journal Fur Die Reine Und Angewandte Mathematik - J REINE ANGEW MATH. 01/2008; 2008(616):1-14.
• Source

  Available from: Guy Metivier

  Article: The Cauchy Problem for Wave Equations with NonLipschitz Coefficients

  Ferruccio Colombini, Guy Metivier
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  ABSTRACT: In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only "Log-Lipschitz" with respect to all the variables. This class of equation is invariant under changes of variables and therefore suitable for a local analysis. In particular, we show local existence, local uniqueness and finite speed of propagation for the noncharacteristic Cauchy problem.
  12/2006;
• Source

  Available from: psu.edu

  Article: A note on two-dimensional transport with bounded divergence

  Ferruccio Colombini, Gianluca Crippa, Jeffrey Rauch
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  ABSTRACT: We prove uniqueness for two dimensional transport across a noncharacteristic curve, under the hypothesis that the vector field is autonomous, bounded and with bounded divergence. We also obtain uniqueness for the Cauchy problem in R t ×R 2 x under an additional condition on the local direction of the vector field.
• Source

  Available from: u-bordeaux.fr

  Article: Exponential growth for the wave equation with compact time-periodic positive potential

  Ferruccio Colombini, Jeffrey Rauch, Vesselin Petkov
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  ABSTRACT: We prove the existence of smooth positive potentials V ( t, x ), periodic in time and with compact support in x , for which the Cauchy problem for the wave equation u tt − Δ x u + V ( t, x ) u = 0 has solutions with exponentially growing global and local energy. Moreover, we show that there are resonances, z ∈ [Copf], [verbar] z [verbar] > 1, associated to V ( t, x ). © 2008 Wiley Periodicals, Inc.
• Source

  Available from: intlpress.com

  Article: Nearly Lipschitzean Divergence Free Transport Propogates neither Continuity nor BV Regularity

  Ferruccio Colombini, Tao Luo, Jeffrey Rauch
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  ABSTRACT: We give examples of divergence free vector fields. For such fields the Cauchy problem for the linear transport equation has unique bounded solutions. The first example has nonuniqueness in the Cauchy problem for the ordinary differential equation defining characteristics. In addition, there are smooth initial data so that the unique bounded solution is not continuous on any neighborhood of the origin. The second example is a field of similar regularity and intial data of bounded variation.