[CvGmt News] Seminario di Analisi Matematica alla SNS

[Luigi Ambrosio]

Aula Contini, Collegio Fermi SNS

Mercoledi' 10 Maggio, ore 15.00

Stefano Bianchini (SISSA)

Titolo: The boundary Riemann solver coming from the real vanishing
viscosity approximation

Abstrac: The following hyperbolic-parabolic approximation
\begin{equation*}
\left\{
\begin{array}{lll}
      \ve_t + \tilde{A} \big( \ve, \, \ee \ve_x \big) \ve_x =
      \ee \tilde{B}(\ve ) \ve_{xx} \qquad \ve \in \mathbb{R}^N\\
      \ve (t, \, 0) \equiv \bar{v}_b \\
      \ve (0, \, x) \equiv \bar{v}_0 \\
\end{array}
\right.
\end{equation*}
of an hyperbolic boundary Riemann problem is considered.
The conservative case is, in particular,
included in the previous formulation.

It is assumed that the approximating solutions $v^{\varepsilon}$
converge in $L^1_{loc}$ to a unique limit, which is supposed to
depend continuously in $L^1$ with respect to the initial and the
boundary data. Moreover, it is assumed that in the hyperbolic
limit the disturbances travel with finite propagation speed.

Under these hypotheses, it is given a complete characterization of
the boundary Riemann solver induced in the hyperbolic limit when
the difference between the boundary and the initial datum is
small. Finally, it is described a way of assigning the boundary datum
which is coherent with the admissibility criterium obtained.

Tutti gli interessati sono invitati a partecipare.

Luigi Ambrosio


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