# Asymptotic Behavior of the Solution to the System for a Viscous Reactive Gas

@article{Guo1999AsymptoticBO, title={Asymptotic Behavior of the Solution to the System for a Viscous Reactive Gas}, author={Boling Guo and Peicheng Zhu}, journal={Journal of Differential Equations}, year={1999}, volume={155}, pages={177-202} }

Abstract In this paper, we investigate the asymptotic behavior of the generalized solution to the compressible Navier–Stokes equations which describes a thermal explosion in a viscous reactive perfect gas confined between two infinite parallel plates in combustion theory.

## 25 Citations

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## References

SHOWING 1-10 OF 29 REFERENCES

### Asymptotic stability of the solutions to a full one-dimensional system of heat-conductive, reactive, compressible viscous gas

- Mathematics
- 1998

We consider the asymptotic behavior of the complete system of equations governing a heat-conductive, reactive, compressible viscous gas in a bounded interval. The motion is proved to exponentially…

### Global a priori estimates for a viscous reactive gas

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 1985

Synopsis A priori estimates on the solution to the complete system of equations governing a heat-conductive, viscous reactive perfect gas confined between two infinite parallel plates are derived.…

### Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids

- Mathematics
- 1983

The equations of motion of compressible viscous and heat-conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region. The…

### Global Smooth Solutions to the Initial-Boundary Value Problem for the Equations of One-Dimensional Nonlinear Thermoviscoelasticity

- Mathematics
- 1982

The system of balance laws of mass, momentum and energy for a class of one-dimensional thermoviscoelastic materials is considered, and the existence of globally defined smooth thermomechanical…

### Global Solutions for the One-Dimensional Equations of a Viscous Reactive Gas.

- Mathematics
- 1984

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…

### Global existence of large solutions to initial boundary value problems for a viscous, heat-conducting, one-dimensional real gas

- Mathematics, Physics
- 1985

### On the Solvability of a Boundary Value Problem for Model Equations of Linearly Viscous Materials

- Mathematics
- 1996

This paper deals with model equations for linearly viscous materials. Viscosity is allowed to vary with temperature. The global solvability of an initial-boundary value problem for nonlinear…

### EXISTENCE THEOREMS FOR THE EQUATIONS OF MOTION OF A COMPRESSIBLE VISCOUS FLUID

- Mathematics
- 1981

One of the fundamental questions that should be answered concerning any problem of mathematical physics is whether it is well set, that is whether solutions actually exist and whether they are…

### Mathematical Problems from Combustion Theory

- Engineering
- 1989

This book develops models of spatially-varying transient processes describing thermal events to predict where the explosion will occur, determine where the hotspots will develop, and finally predict how the hotspot of blowup singularities evolve.

### On the detonation of a combustible gas

- Mathematics
- 1983

This paper is concerned with the existence of detonation waves for a combustible gas. The equations are those of a viscous, heat conducting, polytropic gas coupled with an additional equation which…