Global Solutions for the One-Dimensional Equations of a Viscous Reactive Gas.
Abstract
The behavior of a confined, heat-conductive, viscous, and chemically reactive gas is described by a system of partial differential equations which is of hyperbolic-parabolic type and is highly nonlinear. This paper proves the existence of a unique solution, global in time, for the corresponding initial-boundary value problem. The proof combines a local existence theorem with global a priori bounds on the solutions, and relies on a preliminary estimate for the total free energy of the system. From a physical point of view, these results show that the heat conductivity and the viscosity of the gas prevent shocks from developing, at all positive times, for arbitrarily large Lipschitz continuous initial data.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1984
- Accession Number
- ADA142931
Entities
People
- A. Bressan
Organizations
- University of Wisconsin–Madison