International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Ходжимуродова М.Б.  

To the properties of the solutions of one nonlinear problem of a heat conductivity

The qualitative properties of the problem Cauchy for the equation of nonlinear heat conductivity a with gradient nonlinearity at presence of an absorption is investigated. It is proved, that if the coefficient of heat conductivity includes, time-dependent function that occurs localization of the soluision even an absience of absorption. The Kalashnikov A.S. , Knerr B.F. , Kershner R.. type estimation of a weak solution of the problem Cauchy and an estimation of a free boundary are received..Based on qualitative properties the numerical analysys of solutons carried out