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BV solutions and relaxation limit for a model in viscoelasticity

Published online by Cambridge University Press:  14 November 2011

Tao Luo  and
Roberto Natalini
Tao Luo
Affiliation:
Istituto per le Applicazioni del Calcolo ‘M. Picone’, Viale del Policlinico 137,1-00161 Roma, Italy
Roberto Natalini
Affiliation:
Istituto per le Applicazioni del Calcolo ‘M. Picone’, Viale del Policlinico 137,1-00161 Roma, Italy
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Abstract

Global existence of uniformly bounded BV entropy solutions to a 2 × 2 quasilinear system with relaxation, arising in viscoelasticity, is established by using special fractional step versions of Godunov and Glimm schemes for arbitrarily large initial data. Thanks to the uniform estimates obtained, we prove the convergence of solutions to the corresponding equilibrium limit as the relaxation parameter tends to zero.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 775 - 795
Copyright
Copyright © Royal Society of Edinburgh 1998

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