The well-posedness of the solutions based on the \(L^1\) initial value condition (Q1624143)

Summary: The non-Newtonian polytropic filtration equation \(u_t = \operatorname{div}(a(x) | \nabla u^m |^{p - 2} \nabla u^m)\) is considered. Only if \(u_0(x) \in L^1(\Omega)\), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions.