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- Evers, Joep H.M., et al.
(författare)
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Mild solutions to a measure-valued mass evolution problem with flux boundary conditions
- 2015
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Ingår i: Journal of Differential Equations. - : Elsevier. - 0022-0396 .- 1090-2732. ; 259:3, s. 1068-1097
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0, 1] endowed with a linear discontinuous production term, formulated in the space M([0, 1]) of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem.
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| 2. |
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| 3. |
- Evers, Joep, et al.
(författare)
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Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions
- 2014
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Ingår i: Comptes rendus. Mathematique. - : Elsevier. - 1631-073X .- 1778-3569. ; 352:1, s. 51-54
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Tidskriftsartikel (refereegranskat)abstract
- This Note deals with imposing a flux boundary condition on a non-conservative measure-valued mass evolution problem posed on a bounded interval. To establish the wellposedness of the problem, we exploit particle system approximations of the mass accumulation in a thin layer near the active boundary. We derive the convergence rate for the approximation procedure as well as the structure of the flux boundary condition in the limit problem.
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