ABOUT POSITIVE PERIODICAL SOLUTIONS OF PARABOLIC EQUATIONS

The aim is to investigate the properties of time-periodical solutions of the second order parabolic equations. The existence of the leading natural value in the spectral problem in the limited region with homogeneous boundary Dirichlet condition has been proven. The conditions on the non-existence of the positive time-periodical solutions of the non-linear parabolic equation in the compact exterior have been found. The asymptotic behaviour according to the spatial variables of a number of the second order linear and non-linear parabolic equations has been investigated also. The results can find application in the investigations of the linear and non-linear differential equations and also in the mathematical physics problems. The investigation used the results of theory of parabolic equations, results of the fundamental solutions of the linear parabolic equations with discontinuous coefficientsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio