Finite-dimensional model of thermal instability Original Research Article

Using the collocation method, we derive a finite-dimensional (3-D) dynamical system whose dynamics mimic behavior of a free boundary problem for the heat equation that describes solid combustion and some phase transitions and has been shown to develop complex dynamical patterns. Numerical simulations on the 3-D system demonstrate a variety of dynamical scenarios depending on boundary kinetic functions inherited from the original problem. The multitude of nontrivial dynamical features as well as a clear physical origin of the system make it interesting in its own right.