Special Session 69: Mathematical Models and Analysis of (Partial) Differential Equations in the Applied Sciences

Conservation Laws Constrained by Linear PDEs
Andreas Vikelis
University of Vienna
Austria
Co-Author(s):    
Abstract:
Linear PDE constraints, expressed through constant rank operators, arise naturally in continuum mechanics and impose a specific analytical structure on the admissible states of conservation laws. This structure leads to a natural notion of convexity, acting precisely along the directions in which the operator loses ellipticity. In the talk, it will be discussed how the convexity determined by the PDE constraint, together with the constraint itself, yields robust stability and uniqueness properties for the associated general systems of conservation laws.