131 research outputs found
Unique Continuation for Schr\"odinger Evolutions, with applications to profiles of concentration and traveling waves
We prove unique continuation properties for solutions of the evolution
Schr\"odinger equation with time dependent potentials. As an application of our
method we also obtain results concerning the possible concentration profiles of
blow up solutions and the possible profiles of the traveling waves solutions of
semi-linear Schr\"odinger equations.Comment: 23 page
Uncertainty Principle of Morgan type and Schr\"odinger Evolutions
We prove unique continuation properties for solutions of evolution
Schr\"odinger equation with time dependent potentials. In the case of the free
solution these correspond to uncertainly principles referred to as being of
Morgan type. As an application of our method we also obtain results concerning
the possible concentration profiles of solutions of semi-linear Schr\"odinger
equations
Null-Control and Measurable Sets
We prove the interior and boundary null-controllability of some parabolic
evolutions with controls acting over measurable sets.Comment: Two remarks adde
Hardy uncertainty principle, convexity and parabolic evolutions
We give a new proof of the version of Hardy’s uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds for solutions to the heat equation with Gaussian decay at a future time.We extend the result to heat equations with lower order variable coefficient.IT641-13 (GIC12/96), DMS-0968472, DMS-126524
Hardy's Uncertainty Principle, Convexity and Schr\"odinger Evolutions
We prove the logarithmic convexity of certain quantities, which measure the
quadratic exponential decay at infinity and within two characteristic
hyperplanes of solutions of Schr\"odinger evolutions. As a consequence we
obtain some uniqueness results that generalize (a weak form of) Hardy's version
of the uncertainty principle. We also obtain corresponding results for heat
evolutions
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