The Well-Posedness of the Solutions Based on the L1 Initial Value Condition

الملخص EN

The non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered.

Only if u0(x)∈L1(Ω), 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.