## Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity.(English)Zbl 0709.73013

Summary: A parabolic system arising as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of $$L_{\infty}$$- a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.

### MSC:

 74B20 Nonlinear elasticity 35B65 Smoothness and regularity of solutions to PDEs 35B45 A priori estimates in context of PDEs 35K45 Initial value problems for second-order parabolic systems
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### References:

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