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Creators/Authors contains: "Ancona, Fabio"

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  1. ; ; ; (, Journal of Differential Equations)
    For a scalar conservation law with strictly convex flux, by Oleinik’s estimates the total variation of a solution with bounded measurable initial data decays like 1/t. This paper introduces a class of intermediate domains where a faster decay rate is achieved. A key ingredient of the analysis is a “Fourier-type” decomposition of u into components which oscillate more and more rapidly. The results aim at extending the theory of fractional domains for analytic semigroups to an entirely nonlinear setting. 
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    Free, publicly-accessible full text available March 1, 2026
  2. ; ; ; ; (, Quarterly of Applied Mathematics)
    The paper discusses various regularity properties for solutions to a scalar, 1-dimensional conservation law with strictly convex flux and integrable source. In turn, these yield compactness estimates on the solution set. Similar properties are expected to hold for 2x2 genuinely nonlinear systems. 
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    Full Text Available 
  3. ; ; ; (, Journal of dynamics and differential equations)
    The paper studies a PDE model describing the elongation of a plant stem and its bending as a response to gravity. For a suitable range of parameters in the defining equations, it is proved that a feedback response produces stabilization of growth, in the vertical direction. 
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