Conservation Laws with Dissipation,
Abstract
The conservation laws of isothermal, isentropic or adiabatic thermoelasticity, in all their standard variants (Lagrangean or Euclidean formulation, solids or fluids, one or several space dimensions, etc.), lead to systems of quasilinear hyperbolic equations. A feature of such systems in that the Cauchy problem does not have global smooth solutions, even when the initial data are very smooth, due to the formation of shock waves. However, global solutions exist in the class of functions of bounded variations. A dissipative mechanism may affect, in general, the asymptotic behavior as well as the smoothness of solutions. Ranked according to effectiveness, dissipative mechanisms may be classified into those which are so powerful as to smoothen out even rough initial data, always yielding smooth solutions; those that preserve the smoothness of smooth initial data but are incapable of smoothening rough initial data; those that preserve the smoothness of smooth and 'small' initial data but cannot prevent the breaking of smooth waves of large amplitude; and those that are not capable to prevent even the breaking of smooth waves of small amplitude.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1980
- Accession Number
- ADA088762
Entities
People
- C. M. Dafermos
Organizations
- Brown University