Systems of Evolution Equations in Thermochemical Equations

摘要

In the framework of continuum mechanics the motion of deforming bodies isdescribed by systems of nonlinear evolution equations, that arise by combining balance laws with constitutive relations characterizing the material response. The nonlinear character of the material response often induces a destabilizing mechanism that competes with dissipative mechanisms, such as viscosity or thermal diffusion. As a result of the competition coherent structures may appear, which at some level of modeling manifest themselves as singularities in the solutions of the corresponding model, These structures are diverse in nature, ranging from shock waves to shear bands to propagating phase boundaries, and no common theory can encompass all of them at present. Various instances of such phenomena were studied as part of the project. Specifically (a) A class of test problems intended to test a thermoplastic instability mechanism for shear band formation at high strain rates. (b) Dynamics of spurt phenomena in viscoelastic flows. (c) Self-similar viscous and hydrodynamic limits for the equations of isentropic gas dynamics and the Broadwell system. Shear bands, spurt in viscoelastic flows, self-similar viscous limits; Broadwell model.