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The non-Newtonian polytropic filtration equation is considered. Only if , 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.

journal of function spaces

The Well-Posedness of the Solutions Based on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> Initial Value Condition

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