We consider a scalar, possibly degenerate parabolic equation with a source term, in several space dimensions. For initial data with bounded variation we prove the existence of solutions to the initial-value problem. Then we show that these solutions converge, in the vanishing-viscosity limit, to the Kruzhkov entropy solution of the corresponding hyperbolic equation. The proof exploits the $H$-measure compactness in several space dimensions.
Vanishing Viscosity Limits of Scalar Equations with Degenerate Diffusivity / Corli, A; Coclite, G; di Ruvo, L.. - (2017).
Vanishing Viscosity Limits of Scalar Equations with Degenerate Diffusivity.
Coclite GMembro del Collaboration Group
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2017-01-01
Abstract
We consider a scalar, possibly degenerate parabolic equation with a source term, in several space dimensions. For initial data with bounded variation we prove the existence of solutions to the initial-value problem. Then we show that these solutions converge, in the vanishing-viscosity limit, to the Kruzhkov entropy solution of the corresponding hyperbolic equation. The proof exploits the $H$-measure compactness in several space dimensions.File in questo prodotto:
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