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Award ID contains: 2006884

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  1. ; ; ; ; (, 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 2 x 2 genuinely nonlinear systems. 
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    Accepted Manuscript Full Text Available
  2. ; ; ; (, Communications in partial differential equations)
    This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with H2 regularity away from the shocks plus a corrector term having an asymptotic behavior like x ln x close to each shock. A key step in the analysis is the construction of piecewise smooth solutions with a single shock for a general class of initial data. 
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    Accepted Manuscript Full Text Available
  3. ; ; (, Journal of computational physics)
    In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin. These are different from the multi- dimensional Riemann problems widely studied in the literature. Our computations provide numerical evidence of the existence of initial value problems with multiple solutions, thus revealing a fundamental obstruction toward the well-posedness of the governing equations. The compressible Euler equations are solved using the positivity-preserving discontinuous Galerkin method. 
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    Full Text Available 
  4. ; ; (, Archive for Rational Mechanics and Analysis)
    null (Ed.)
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  5. ; (, Communications in Mathematical Sciences)
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