On an anisotropic parabolic equation on the domain with a disjoint boundary (Q1749085)

The paper under review deals with stability issues regarding the anisotropic parabolic equation with variable exponent growth \[ \begin{cases} v_t = \sum_{i = 1}^n\left(b_i(x)|v_{x_i}|^{q_i(x) - 2} v_{x_i}\right)_{x_i} & (x,t)\in Q_T=\Omega\times(0,T),\\ v(x,0)=v_0(x) & x\in\Omega,\\ v(x,t)=0 & (x,t)\in \Sigma_p\times(0,T), \end{cases} \] where \(b_i(x),q_i(x) \in C^1(\overline{\Omega}),\) \(q_i(x) > 1,\) \(b_i(x) \geq 0\) and \(\Sigma_p\) is a part of \(\partial\Omega\) where \(b_i(x)\geq c_i>0,\) while \(b_i(x)=0\) on \(\partial\Omega\setminus\Sigma_p.\) The results announced seem doubtful to this reviewer.