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Vanishing viscosity solutions of a 2 x 2 triangular hyperbolic system with Dirichlet conditions on two boundaries

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dc.contributor.author Spinolo, Laura en_US
dc.date.accessioned 2005 en_US
dc.date.accessioned 2011-09-07T20:27:43Z
dc.date.available 2005 en_US
dc.date.available 2011-09-07T20:27:43Z
dc.date.issued 2005 en_US
dc.identifier.citation Indiana Univ. Math. J. 56 (2007) 279-364 en_US
dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/1731 en_US
dc.description.abstract We consider the 2 x 2 parabolic systems [] on a domain (t, x) [] with Dirichlet boundary conditions imposed at x = 0 and at x = l. The matrix A is assumed to be in triangular form and strictly hyperbolic, and the boundary is not characteristic, i.e. the eigenvalues of A are different from 0. We show that, if the initial and boundary data have sufficiently small total variation, then the solution [] exists for all [] and depends Lipschitz continuously in L1 on the initial and boundary data. Moreover, as [], the solutions [] converge in L1 to a unique limit u(t), which can be seen as the vanishing viscosity solution of the quasilinear hyperbolic system []. This solution u(t) depends Lipschitz continuously in L1 w.r.t the initial and boundary data. We also characterize precisely in which sense the boundary data are assumed by the solution of the hyperbolic system. en_US
dc.format.extent 571395 bytes en_US
dc.format.mimetype application/pdf en_US
dc.language.iso en_US en_US
dc.relation.ispartofseries SISSA;60/2005/M en_US
dc.relation.ispartofseries arXiv.org;math.AP/0508142 en_US
dc.relation.uri 10.1512/iumj.2007.56.2843 en_US
dc.title Vanishing viscosity solutions of a 2 x 2 triangular hyperbolic system with Dirichlet conditions on two boundaries en_US
dc.type Preprint en_US
dc.contributor.department Functional Analysis and Applications en_US
dc.contributor.area Mathematics en_US


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