Paolo Secchi

Well-posedness of characteristic symmetric hyperbolic systems

We consider the initial-boundary-value problem for quasi-linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. We show the well-posedness in Hadamards sense (i.e., existence, uniqueness and continuous dependence of solutions on the data) of regular solutions in suitable functions spaces which take into account the loss of regularity in the normal direction to the characteristic boundary.

Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system

SummaryWe show that the weak solutions of the nonlinear hyperbolic system

On the singular incompressible limit of inviscid compressible fluids

\left\{ \begin{gathered} \varepsilon u_t^\varepsilon + p(v^\varepsilon )_x = u^\varepsilon \hfill \\ v_t^\varepsilon - u_x^\varepsilon = 0 \hfill \\ \end{gathered} \right.

On the motion of viscous fluids in the presence of diffusion

converge, as ε tends to zero, to the solutions of the reduced problem

Global existence for two regularized MHD models in three space-dimension

\left\{ \begin{gathered} u + p(v)_x = 0 \hfill \\ v_t - u_x = 0 \hfill \\ \end{gathered} \right.

On the transition to instability for compressible vortex sheets

. Then they satisfy the nonlinear parabolic equation