Maximum estimates for generalized Forchheimer flows in heterogeneous porous media. (English) Zbl 1366.35124
This paper deals with maximum estimates for generalized Forchheimer flows in heterogeneous porous media, governed by an initial boundary value problem involving a nonlinear PDE which can exhibit different types of degeneracy and singularity. Certain local in time estimates are established. The asymptotic estimates, as time goes to infinity, are discussed in view of the boundary data. It is remarked that in case of homogeneous porous media, estimates for p and its time derivative pave the way for obtaining \(L^\infty\)-estimates for the gradient, as well as strong continuous dependence and structural stability; however, it is not known whether such results still hold true for heterogeneous media in the current study.
Reviewer: Vishnu Dutt Sharma (Mumbai)
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 35B45 | A priori estimates in context of PDEs |
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