On conservation laws in generalized dynamic thermoelasticity

The differential equations of generalized dynamic thermoelasticity constitute a coupled non-self-adjoint system of PDEs, which in its variational form does not admit a Lagrangian. However following exterior calculus methodology, we augment the space of dependent variables, accompanying the initial differential equations with suitable adjoint equations and additional auxiliary “fields”. So the construction of a Lagrangian is now possible along with the realization of Noether's theory for finding conservation laws. Finally, in our case, it is possible to characterize the additional dependent variables in terms of the physical fields themselves and obtain then conservation laws expressed via the original known thermoelastic fields.