We study the limiting behaviour of the Cauchy problem for a class of Carleman-like models in the diffusive scaling with data in the spaces $L^p$, $1 \leq p \leq \infty$. We show that, in the limit, the solution of such models converges towards the solution of a nonlinear diffusion equation with initial values determined by the data of the hyperbolic system. When the data belong to $L^1$, a condition of conservation of mass is needed to uniquely identify the solution in some cases, whereas the solution may disappear in the limit in other cases.
The diffusive limit for Carleman-type kinetic models
SALVARANI, FRANCESCO;
2005-01-01
Abstract
We study the limiting behaviour of the Cauchy problem for a class of Carleman-like models in the diffusive scaling with data in the spaces $L^p$, $1 \leq p \leq \infty$. We show that, in the limit, the solution of such models converges towards the solution of a nonlinear diffusion equation with initial values determined by the data of the hyperbolic system. When the data belong to $L^1$, a condition of conservation of mass is needed to uniquely identify the solution in some cases, whereas the solution may disappear in the limit in other cases.File in questo prodotto:
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