An evaluation of a solution of the Cauchy problem of the nonlinear fractional diffusion equation

In the work, the Cauchy problem for the nonlinear fractional diffusion equation is examined. By connecting the harmonic continuation of the studied solution and the solution itself in one boundary value problem, the desired solution in uniform metrics is evaluated through the integral norm. This proves the substantial limitation of the solution. This evaluation is obtained by sampling functions in an integral identity, where the continuation of the solution and the solution of the differential equation itself are combined in a single integral identity. The method used shows that for small values of time, the behaviour of the solution does not depend on the parameters of the problem. The dependence on the parameters of the problem appears at large values of time, that is, the solution depends on the degree of the source only starting from a certain point in time. From the proved theorem, it is possible to define this moment of time as the solution of some equation. The obtained evaluation is a generalization of similar results obtained for differential equations of a porous medium.