Results 21 to 30 of about 3,628,509 (295)
Concavity of Solutions of the Porous Medium Equation [PDF]
Transactions of the American Mathematical Society, 1987 We consider the problem \[ ( P )
Benilan, Philippe, Vazquez, Juan Luis
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A General Fractional Porous Medium Equation [PDF]
Communications on Pure and Applied Mathematics, 2012 AbstractWe develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion: \input amssym $$\left\{ {\matrix{ {{{\partial u} \over {\partial t}} + \left( { ‐ \Delta } \right)^{\sigma /2} \left( {\left| u \right|^{m ‐ 1} u} \right) = 0,} \hfill & {x \in {\Bbb R} ^N ,\,\,t > 0,} \hfill \cr {u\
De Pablo, Arturo +3 more
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The fractional porous medium equation on the hyperbolic space [PDF]
Calculus of Variations and Partial Differential Equations, 2020 We consider the nonlinear degenerate parabolic equation of porous medium type, whose diffusion is driven by the (spectral) fractional Laplacian on the hyperbolic space. We provide existence results for solutions, in an appropriate weak sense, for data belonging either to the usual $L^p$ spaces or to larger (weighted) spaces determined either in terms ...
Berchio, Elvise +3 more
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Quenching for Porous Medium Equations
Tamkang Journal of Mathematics, 2021 This paper studies the following two porous medium equations with singular boundary conditions. First, we obtain that finite time quenching on the boundary, as well as kt blows up at the same finite time and lower bound estimates of the quenching time of the equation kt = (kn)xx + (1 − k)−α, (x,t) ∈ (0,L) × (0,T) with (kn)x (0,t) = 0, (kn)x (L,t) = (
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Weak Solutions of the Porous Medium Equation [PDF]
Transactions of the American Mathematical Society, 1993 We show that if u ≥ 0
Dahlberg, Björn E. J., Kenig, Carlos E.
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Modelling and simulation of waves in three-layer porous media [PDF]
Nonlinear Processes in Geophysics, 2013 The propagation of gravity waves in an emerged three-layer porous medium is considered in this paper. Based on the assumption that the flow can be described by Darcy's Law, an asymptotic theory is developed for small-amplitude long waves. This leads to a
S. R. Pudjaprasetya
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Porous Medium Equation with a Drift: Free Boundary Regularity [PDF]
Archive for Rational Mechanics and Analysis, 2021 39 pages, 1 ...
Kim, Inwon, Zhang, Yuming Paul
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Equivalence between volume averaging and moments matching techniques for mass transport models in porous media. [PDF]
, 2010 This paper deals with local non-equilibrium models for mass transport in dual-phase and dual-region porous media. The first contribution of this study is to formally prove that the time-asymptotic moments matching method applied to two-equation models is
Davit, Yohan +5 more
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The difference between semi-continuum model and Richards’ equation for unsaturated porous media flow
Scientific Reports, 2022 Semi-continuum modelling of unsaturated porous media flow is based on representing the porous medium as a grid of non-infinitesimal blocks that retain the character of a porous medium. This approach is similar to the hybrid/multiscale modelling.
Rostislav Vodák +3 more
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Natural convection and the evolution of a reactive porous medium [PDF]
, 2011 We describe a mathematical model of buoyancy-driven flow and solute transport in a saturated porous medium, the porosity and permeability of which evolve through precipitation and dissolution as a mineral is lost or gained from the pore fluid. Imposing a
Ritchie, Lindsey Thomson +1 more
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