Ma'lumot

THE DIFFUSION EQUATION IN NON-HOMOGENEOUS MEDIUM WITH TIME DEPENDENCY

M.Bobokandov


The property of a finite speed of a perturbation distribution to the Cauchy problem
for non-divergence form of the parabolic equation based on comparison method and asymptotic
behavior of a self-similar solution is achieved. Defined the conditions for the availability of blow-ups
and global solutions to a given problem using Hopf’s maximum principle for the parabolic equation in
non-homogeneous medium not in divergence form. The resulting asymptotics has been used as an
initial approximation and numerical solutions have been calculated.



https://doi.org/10.59251/2181-1296.v5.1351.1108

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