A spectrum of self-similar solutions of the nonlinear equation of heat transfer in a medium with a volume distributed source is investigated. The self-similar solutions develop in a ‘blow-up’ regime and represent non-stationary dissipative structures. Complex two-dimensional structures containing holes within themselves, i.e. areas of null temperature, and constituting multiply connected areas of burning are studied in the present work. When using numerical algorithms of parameter continuation, the bifurcation analysis is carried out; and evolution of complex two-dimensional structures depending on parameters is explored. Some bifurcations leading to appearance the multiply connected structures containing holes are investigated.

Mathematical modelling in actual problems of science and technics