Abstract:
The following quasilinear parabolic equation with a source term and an inhomogeneous density is considered:
$$
\rho(x)\frac{\partial u}{\partial t}=\operatorname{div}(u^{m-1}|Du|^{\lambda-1}Du)+u^p.
$$
The conditions on the parameters of the problem are found under which the solution to the Cauchy problem blows up in a finite time. A sharp universal (i.e., independent of the initial function) estimate of the solution near the blowup time is obtained.
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