$L_1$–$L_\infty$ estimates of solutions of the Cauchy
problem for an anisotropic degenerate parabolic equation with double
non-linearity and growing initial data
Abstract:
The Cauchy
problem for a degenerate parabolic equation with
anisotropic $p$-Laplacian and double
non-linearity is considered.
For increasing initial data local estimates for the
$L_\infty$-norm of a solution are obtained, which
yield a precise characterization of the growth of solutions at
infinity. An estimate for the order of the length of the time
interval on which a solution
is defined is found in its dependence on the initial data.
Bibliography: 12 titles.
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