BOUNDARY PROBLEMS WITH AMPLIFICATION AND ATTENUATION FACTORS OF NON-LINEAR EFFECTS

The aim is to investigate the solutions of the boundary problems for some classes of the non-linear equations with partial derivatives. The general sign uniting the studied objects is the presence of both factor favourable to the certain non-linear effect and counteracting factor in each of them. The series of the accurate theorems about dependence of the properties for solutions of the non-linear parabolic equations in the unlimited fields upon the behaviour of the coefficients on the infinity has been proved. The qualitative investigation of solving parabolic equations with linearities of the changing shape has been performed. The accurate conditions on the presence of a number of the non-linear effects have been found for non-linear systems of different types. The classes of the implicit-degenerative parabolic and elliptic equations containing the non-linear power functions with small parameter in the indices have been distinguished and investigated. Application field: theory of differential equations, theory of diffusion and heat conduction, underground hydrodynamics, biophysics, synergetics, physics of plasma.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio