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Quasilinear continuity equations of measures for bounded BV vector fields

Lorenz, Thomas

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Abstract

The focus of interest here is a quasilinear form of the conservative continuity equation d/dt v + D·(f(v, ·) v) = 0 (in R^N× ]0, T[) together with its measure-valued distributional solutions. On the basis of Ambrosio’s results about the nonautonomous linear equation, the existence and uniqueness of solutions are investigated for coefficients being bounded vector fields with bounded spatial variation and Lebesgue absolutely continuous divergence in combination with positive measures absolutely continuous with respect to Lebesgue measure. The step towards the nonlinear problem here relies on a further generalization of Aubin's mutational equations that is extending the notions of distribution-like solutions and "weak compactness" to a set supplied with a countable family of (possibly non–symmetric) distance functions (so–called ostensible metrics).

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 22 Jan 2005 13:55
Date: 2005
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Kontinuitätsgleichung, Quasilineare partielle Differentialgleichung, Maß <Mathematik>, Distribution <Funktionalanalysis>
Uncontrolled Keywords: conservative continuity equation , measure-valued distributional solution , generalized ODE on sets with nonsymmetric distances , mutational equations
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