Cauchy problem for a quasilinear parabolic equation with a source term and an inhomogeneous density
А. В. МартыненкоInstitute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. R. Luxemburg 74, Donetsk, 83114, UkraineAnatoli F. TedeevInstitute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. R. Luxemburg 74, Donetsk, 83114, Ukraine
2007en
ABI
Abstract
The following quasilinear parabolic equation with a source term and an inhomogeneous density is considered: $$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + u^p $$ . 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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