Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

DST2012

Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics

​S. Demoulini, A.E. Tzavaras, D. Stuart, Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics, Arch. Rational Mech. Analysis 205 (2012), 927-961.
S. Demoulini, D. Stuart, A.E. Tzavaras
polyconvex elastodynamics
2012
​For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of a dissipative measure-valued solution and show that such a solution agrees with a classical solution with the same initial data, when such a classical solution exists. As an application of the method we give a short proof of strong convergence in the continuum limit of a lattice approximation of one dimensional elastodynamics in the presence of a classical solution. Also, for a system of conservation laws endowed with a positive and convex entropy, we show that dissipative measure-valued solutions attain their initial data in a strong sense after time averaging.