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Award ID contains: 2306926

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  1. ; ; (, Mathematical Models and Methods in Applied Sciences)
    This paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions, depending on the sign of the gradient of the solution. We study here the stable case where solutions form a contractive semigroup in L^1. In the spatially periodic case, we prove that semigroup trajectories coincide with the unique limits of a suitable class of vanishing viscosity approximations. 
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    Free, publicly-accessible full text available June 1, 2026
  2. ; ; ; (, 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
  3. (, Journal of Hyperbolic Differential Equations)
    This paper intends to provide a brief review of the current well-posedness theory for hyperbolic systems of conservation laws in one space dimension, also pointing out open problems and possible research directions. 
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