P.I. will study some free interface problems modeling combustion and phase transitions which generate complex dynamics even in 1-D evolution. He will prove global in time existence of classical solutions and stability for Hopf bifurcation. He will obtain numerically a complete dynamical portrait including sequences of period doubling and transition to chaos, infinite period bifurcations, Silnikov type dynamics etc. Finite-D system modeling entire variety of their dynamics will be derived and studied. P.I. will also study numerically and analytically dynamics generated by a number of invariant surface evolution equations. The equations model basic instabilities in flames and demonstrate formation of nontrivial patterns such as cellular structures, self-turbulence, spiral waves etc. P.I. will study rigorously and numerically several problems modeling propagation of flames, solidification fronts and laser induced evaporation. These processes are known to generate complex dynamical patterns, both temporal and spacial. P.I will obtain numerically a complete dynamical portrait of a variety of regular and chaotic pulsating regimes associated with plane evolution. P.I. will also study numerically and analytically dynamics generated by a number of surface evolution equations. The equations model basic instabilities in flame propagation and demonstrate formation of nontrivial patterns such as cellular structures, self-turbulence, spiral waves etc.
