Global Existence for the Confined Muskat Problem
نویسندگان
چکیده
منابع مشابه
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an L(R) maximum principle, in the form of a new “log” conservation law (3) which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence of Lipschitz continuous sol...
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The Muskat, or Muskat-Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele-Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable,...
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برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولPorous media: the Muskat problem in 3D
The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.
متن کاملThe Domain of Parabolicity for the Muskat Problem
Abstra t. We address the well-posedness of the Muskat problem in a periodi geometry and in a setting whi h allows us to onsider general initial and boundary data, gravity e e ts, as well as surfa e tension e e ts. In the absen e of surfa e tension we prove that the Rayleigh-Taylor ondition identi es a domain of paraboli ity for the Muskat problem. This property is used to establish the well-pos...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2014
ISSN: 0036-1410,1095-7154
DOI: 10.1137/130912529