Siberian Federal University 
- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2015 8 (2)
- Authors
- Raimbekov, Jakhongir R.
- Contact information
- Raimbekov, Jakhongir R.:National University of Uzbekistan Yunus Abad-17, 3/66, 10037 Tashkent, Uzbekistan;
- Keywords
- nonlinear degenerate parabolic equation; non-divergent form; self-similar solution; asymptotic behavior of solutions
- Abstract
We investigate the solutions for the following nonlinear degenerate parabolic equation in non-divergent form with density |x|n @u @t = umdiv |∇u|p−2 ∇u We discuss the properties, which are different from those for the equations in divergence form, thus generalizing various known results. Then getting a self-similar solution we show the asymptotic behavior of solutions at t → ∞. Slow and fast diffusion cases are investigated. Finally, we present the results of some numerical experiments
- Pages
- 192–200
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/16806
Journal of Siberian Federal University. Mathematics & Physics / The Properties of the Solutions for Cauchy Problem of Nonlinear Parabolic Equations in Non-Divergent Form with Density
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