Browsing by Author "Spinolo, Laura"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Characteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations
    (SISSA, 2018-10-16) Bianchini, Stefano; Spinolo, Laura; Mathematics
    We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.
  • Thumbnail Image
    Item
    Invariant Manifolds for Viscous Profiles of a Class of Mixed Hyperbolic-Parabolic Systems
    (2008-12-15T12:03:09Z) Bianchini, Stefano; Spinolo, Laura; Mathematics; Functional Analysis and Applications
  • Thumbnail Image
    Item
    Vanishing viscosity solutions of a 2 x 2 triangular hyperbolic system with Dirichlet conditions on two boundaries
    (2005) Spinolo, Laura; Mathematics; Functional Analysis and Applications
    We consider the 2 x 2 parabolic systems [] on a domain (t, x) [] with Dirichlet boundary conditions imposed at x = 0 and at x = l. The matrix A is assumed to be in triangular form and strictly hyperbolic, and the boundary is not characteristic, i.e. the eigenvalues of A are different from 0. We show that, if the initial and boundary data have sufficiently small total variation, then the solution [] exists for all [] and depends Lipschitz continuously in L1 on the initial and boundary data. Moreover, as [], the solutions [] converge in L1 to a unique limit u(t), which can be seen as the vanishing viscosity solution of the quasilinear hyperbolic system []. This solution u(t) depends Lipschitz continuously in L1 w.r.t the initial and boundary data. We also characterize precisely in which sense the boundary data are assumed by the solution of the hyperbolic system.