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hal.structure.identifierGran Sasso Science Institute [GSSI]
dc.contributor.authorMarchesani, Stefano*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorOlla, Stefano
HAL ID: 18345
ORCID: 0000-0003-0845-1861
*
dc.date.accessioned2020-04-23T08:57:49Z
dc.date.available2020-04-23T08:57:49Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20652
dc.language.isoenen
dc.subjectClausius inequality
dc.subjectcom- pensated compactness
dc.subjectentropy solutions
dc.subjectboundary conditions
dc.subjectweak solutions
dc.subjecthydrodynamic limits
dc.subjectisothermal Euler equation
dc.subjectnon-linear wave equa- tion
dc.subject.ddc520en
dc.titleHydrodynamic Limits and Clausius inequality for Isothermal Non-linear Elastodynamics with Boundary Tension
dc.typeDocument de travail / Working paper
dc.description.abstractenWe consider a chain of particles connected by an-harmonic springs, with a boundary force (tension) acting on the last particle, while the first particle is kept pinned at a point. The particles are in contact with stochastic heat baths, whose action on the dynamics conserves the volume and the momentum, while energy is exchanged with the heat baths in such way that, in equilibrium, the system is at a given temperature T. We study the space empirical profiles of volume stretch and momentum under hyperbolic rescaling of space and time as the size of the system growth to be infinite, with the boundary tension changing slowly in the macroscopic time scale. We prove that the probability distributions of these profiles concentrate on L^2-valued weak solutions of the isothermal Euler equations (i.e. the non-linear wave equation, also called p-system), satisfying the boundary conditions imposed by the microscopic dynamics. Furthermore, the weak solutions obtained satisfy the Clausius inequality between the work done by the boundary force and the change of the total free energy in the system. This result includes the shock regime of the system.
dc.publisher.nameCahier de recherche CEREMADE, Université Paris-Dauphine
dc.publisher.cityParisen
dc.identifier.citationpages43
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris-Dauphine
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-02447255
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.identifier.citationdate2020
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dc.description.audienceInternational
dc.date.updated2020-05-12T11:53:52Z
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