| Popis: |
We show that a locally bounded nonnegative weak solution of the general double degenerate parabolic equation u t − div a ( x , t , u , ∇ u ) = b ( x , t , u , ∇ u ) , satisfying the structure conditions a ( x , t , u , u ) ⋅ u ≥ ϕ ( | u | ) | u | 2 − φ 0 ( x , t ) , | a ( x , t , u , u ) | ≤ ϕ ( | u | ) | u | + ϕ 1 2 ( | u | ) φ 1 ( x , t ) , | b ( x , t , u , u ) | ≤ ϕ ( | u | ) | u | + φ 2 ( x , t ) , being ϕ a continuous function vanishing in u = 0 and u = 1 , is locally continuous, generalizing therefore the study of the local regularity theory for the saturation in the flow of two immiscible fluids in a porous medium presented in DiBenedetto et al. (in press) [16] . |
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