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A singular asymptotic behavior of a transport equation. (English) Zbl 1134.35008

Summary: We consider a simple conservative transport equation where the speed is strictly decreasing. The monotonicity property of the speed rate leads to a singular asymptotic behavior and the concentration of the mass of the solution at a point. Thus, a model which contains a transport structure with monotone decay of the speed rate can be reduced by using the result of convergence to a Dirac mass. It is useful in the case where we have to simulate numerous nonlinear PDEs containing such a structure. Indeed, the concentration of the mass makes the variable in which the mass concentrate useless and thus we lose a dimension. The gain in time calculus is important when the number of equations is large.

MSC:

35A20 Analyticity in context of PDEs
82C70 Transport processes in time-dependent statistical mechanics
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