Geodesic
Metastability for scalar conservation laws in a bounded domain
Corrado Mascia1, 2 ; Marta Strani3
1 Dipartimento di Matematica “G. Castelnuovo”, Sapienza – Università di Roma, P.le Aldo Moro, 2 - 00185 Roma (ITALY),
2 Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche (associated in the framework of the program “Intracellular Signalling”)
3 Ecole Normale Supérieure, Département de Mathématiques et Applications, 45 rue d’Ulm - 75005 Paris (France),
ESAIM. Proceedings, Tome 45 (2014), pp. 247-254 Cet article a éte moissonné depuis la source EDP Sciences

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The initial-boundary-value problem for a viscous scalar conservation law in a bounded interval I = ( − ℓ,ℓ) is considered, with emphasis on the metastable dynamics, whereby the time-dependent solution develops internal transition layers that approach their steady state in an asymptotically exponentially long time interval as the viscosity coefficient ε> 0 goes to zero. We describe such behavior by deriving an ODE for the position ξ of the internal interface. The main tool of our analysis is the construction of a one-parameter family of approximate stationary solutions {Uεε(.;ξ)}ξ∈I, parametrized by the location of the shock layer ξ, to be considered as an approximate invariant manifold for the problem. By using the properties of the linearized operator at Uε, we estimate the size of the layer location.
DOI : 10.1051/proc/201445025

Corrado Mascia 1, 2 ; Marta Strani 3

1 Dipartimento di Matematica “G. Castelnuovo”, Sapienza – Università di Roma, P.le Aldo Moro, 2 - 00185 Roma (ITALY),
2 Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche (associated in the framework of the program “Intracellular Signalling”)
3 Ecole Normale Supérieure, Département de Mathématiques et Applications, 45 rue d’Ulm - 75005 Paris (France), 
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     author = {Corrado Mascia and Marta Strani},
     title = {Metastability for scalar conservation laws in a bounded domain},
     journal = {ESAIM. Proceedings},
     pages = {247--254},
     year = {2014},
     volume = {45},
     doi = {10.1051/proc/201445025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201445025/}
}
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Corrado Mascia; Marta Strani. Metastability for scalar conservation laws in a bounded domain. ESAIM. Proceedings, Tome 45 (2014), pp. 247-254. doi: 10.1051/proc/201445025

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