arXiv subjects
Publications and source records attributed to M. Frankel.
Solutions of a 1-D free-interface problem modeling solid combustion front propagating in combustible mixture with periodically varying concentration of reactant exhibit classical phenomenon of mode locking. Numerical simulation shows a variety of locked periodic, quasi-periodic and chaotic solutions.
We study a free interface problem related to combustion of condensed matter and some non-equilibrium exothermal phase transitions. In spite of a variety of non-trivial dynamical scenarios exhibited by the model the solutions are uniformly bounded and the interface velocity is a smooth function. The main result of the paper establishes existence of a compact connected attractor for the classical solutions of the problem. Numerical evidence leads to the conjecture that the fractal dimension of the attractor is finite.