By Goursat E.
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Extra resources for A course in mathematical analysis. - part.2 Differential equations
This result was treated in detail in [A1]. 35 FLOWS INNON-LINEAR POROUS MEDIA GEOMETRIC METHODS NON-LINEAR IN THE ANALYSIS OF FLOWS IN POROUS MEDIA9 In the next section we will introduce a few basic geometric notions and definitions, in order to show the robust link between these two objects. The actual relationship between the two equations is far from being straight-forward, in spite of their similarity. In particular, we will show that the pressure function can be interpreted as a CMC graph under some constraints and appropriate geometric transformations.
It is straight-forward to extend this to manifolds with corners. 1 (Borel). Let M be a manifold with a (boundary intersection free) G-action with a unique isotropy type, if N (K) is the normalizer of an isotropy group K then M is G-equivariantly diﬀeomorphic to G×N (K) M K and the inclusion M K → M induces a diﬀeomorphism (N (K)/K)\M K = N (K)\M K ∼ = G\M. 22 PIERRE ALBIN AND RICHARD MELROSE Proof. 7] in the boundaryless case. 2 that for a ﬁxed isotropy group M K is a smooth interior p-submanifold.
Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, Springer-Verlag, (1980). 42 16 EUGENIO AULISA, AKIF IBRAGIMOV, AND MAGDALENA TODA [S2] M. Spivak, Diﬀerential geometry, vol. I and II, 2nd Edition, Publish or Perish, 1977. P. Tavera, H. Kazemi, E. Ozkan, Combine eﬀect of Non-Darcy Flow and Formation Damage on Gas Well Performance of Dual-Porosity and Dual Permeability Reservoirs, SPE90623, 2004. [W] S. Whitaker, The Forchheimer Equation: A Theoretical Development, Transport in Porous Media 25: 27–61 (1996).
A course in mathematical analysis. - part.2 Differential equations by Goursat E.