The first order conservation laws for an arbitrary homogeneous linear planar elastic material are completely classified. In all cases, both isotropic and anisotropic, besides the standard Betti reciprocity laws, there are two infinite-dimensional families of conservation laws, each depending on an arbitrary analytic function of two complex variables.

We give a new convergence proof for finite volume schemes approximating scalar conservation laws. The main ingredients of the proof are the kinetic formulation of scalar conservation laws, a discrete entropy inequality, and the velocity averaging technique.

In this survey paper, we present and analyze some topics in the theory of quasilinear partial differential equations denominated Conservation Laws. In addition, we present some important examples of systems and scalar conservation laws.

In nonholonomic dynamics, symmetries do not always lead to conservation laws. In this paper we study conditions for a nonholonomic system with symmetry to have conservation laws linear in momentum.

4 Caveat Emptor 7 4.1 Lagrangian Wanted . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Not Quite a Conservation Law . . . . . . . . . . . . . . . . . . 7 4.3 Inequivalent Lagrangians . . . . . . . . . . . . . . . . . . . . . 7 4.4 Other Conservation Laws . . . . . . . . . . . . . . . . . . . . . 8 4.4.1 Dynamical Conservations Laws . . . . . . . . . . . . . 8 4.4.2 Solitons . . . . . . ....