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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.
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Luo et al. (1998) studied this question.
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