From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity

We prove non existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Nonlinear Elasticity. This system is of mixed elliptic-hyperbolic type. We discuss also a relation of such a system to polynomial integrals of Classical Hamiltonian systems.

💡 Research Summary

The paper investigates a quasi‑linear system of partial differential equations that arises in Ericksen’s model of nonlinear elasticity. This system couples a scalar displacement field with an internal director (or orientation) field and is of mixed elliptic‑hyperbolic type: depending on the state variables, the coefficient matrix possesses both real and complex eigenvalues. The authors first derive the system from a variational principle, showing that the governing equations can be written in the form
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