Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

BV solutions and relaxation limit for a model in viscoelasticity

Tao Luoa1 p1 and Roberto Natalinia1

a1 Istituto per le Applicazioni del Calcolo ‘M. Picone’, Viale del Policlinico 137,1-00161 Roma, Italy

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.

(Received September 27 1996)

Correspondence

p1 Permanent address: Institute of Mathematics, Academia Sinica, Beijing 100080, P.R. China. Supported by CNR Italy under Grant n.211.01.29 on 6.8.1994