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Estimates for Conservation Laws with Little Viscosity
Constantine M. Dafermos
Source abstract
We consider the parabolic system that is generated by adding “artificial viscosity” to the equations of one-dimensional nonlinear elasticity. We construct families of entropies that induce a priori bounds on solutions, independent of the viscosity. The entropies have exponential growth in the case of strain hardening and polynomial growth in the case of strain softening. In particular, we recover the standard theory of invariant regions.
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