| Autor: |
Martynenko, Aleksandr V, Tedeev, Anatoli F, Shramenko, Vladimir N |
| Zdroj: |
Izvestiya: Mathematics; June 2012, Vol. 76 Issue: 3 p563-580, 18p |
| Abstrakt: |
Given a degenerate parabolic equation of the form $ \rho(x) u_t=\operatorname{div}(u^{m-1}\vert Du\vert^{\lambda-1}Du)+\rho(x)u^p$ with a source and inhomogeneous density, we consider the Cauchy problem with an initial function slowly tending to zero as $ \vert x\vert \to \infty$. We find conditions for the global-in-time existence or non-existence of solutions of this problem. These conditions depend essentially on the behaviour of the initial data as $ \vert x\vert \to \infty$. In the case of global solubility we obtain a sharp estimate of the solution for large values of time. |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
|
