A nonlinear parabolic problem from combustion theory: attractors and stability. (English) Zbl 1083.35023
A parabolic (convection-diffusion) problem in a half-line, arising when modeling the temperature profile of an adiabatic solid in radation-driven combustion, is considered. The authors refer to solid-propellant rocket propulsion theory, when modelling combustion of homogeneous materials under the influence of external irradiation of the “interface” between condensed and gas phases. The evolution semigroup associated with the problem is properly defined and uniform boundedness of the solution at large time and existence of absorbing sets are proved. It is proven that there exists a global attractor for the evolution semigroup associated with the problem. Finally, the stabilization of all solutions towards the equilibrium solution is derived for a class of Neumann data, which are of some interest for applications.
Reviewer: Abdolrahman Razani (Qazvin)
MSC:
| 35B41 | Attractors |
| 35K55 | Nonlinear parabolic equations |
| 37L30 | Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems |
| 80A25 | Combustion |
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