Decay of the Solutions of Parabolic Equations with Double Nonlinearity and the Degenerate Absorption Potential - Stepanova, E. V. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
We study the behavior of solutions for the parabolic equation of nonstationary diffusion with double nonlinearity and a degenerate absorption term: $$ {\left({\left| u\right|}^{q-1} u\right)}_t-{\displaystyle \sum_{i=1}^N\frac{\partial }{\partial {x}_i}\left({\left|{ abla}_x u\right|}^{q-1}\frac{\partial u}{\partial {x}_i}\right)+{a}_0(x){\left| u\right|}^{λ -1} u=0,} $$ where \( {a}_0(x)\ge {d}_0\; \exp \left(-\frac{ω \left(\left| x\right|\right)}{{\left| x\right|}^{q+1}}\right) \) , d 0 = const > 0, 0 ≤ λ 0 for τ > 0, and \( {\displaystyle {\int}_{0+}\frac{ω \left(τ \right)}{τ} dτ