Pliukhin O. Conditional symmetries and exact solutions of reaction-diffusion systems with power coefficients of diffusion

The thesis is devoted to searching of Q-conditional symmetries of reaction-diffusion-convection nonlinear equations with power nonlinearities and nonlinear reaction-diffusion systems with constant and power coefficients diffusions; constructing exact solutions of reaction-diffusion-convection equations and reaction-diffusion systems. A complete description of Q-conditional symmetries for reaction-diffusion–convection equations with power diffusivities is derived. It is shown that all the known results for reaction–diffusion equations with power diffusivities follow as particular cases from those obtained in the thesis but not vice versa. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. In the particular case, new exact solutions of nonlinear reaction–diffusion-convection equations arising in application and their natural generalizations are found. A wide range of new Q-conditional symmetries for reaction–diffusion systems with power diffusivities are constructed.The relevant non-Lie ansatze to reduce the reaction–diffusion systems to ODE systems and examples of exact solutions are obtained. The relation of the solutions obtained with the development of spatially inhomogeneous structures is discussed.