Results 11 to 20 of about 221,531 (271)
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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p-Adic Analogue of the Porous Medium Equation [PDF]
Journal of Fourier Analysis and Applications, 2017 We consider a nonlinear evolution equation for complex-valued functions of a real positive time variable and a p-adic spatial variable. This equation is a non-Archimedean counterpart of the fractional porous medium equation. Developing, as a tool, an $L^1$-theory of Vladimirov's p-adic fractional differentiation operator, we prove m-accretivity of the ...
Andrei Yu. Khrennikov +1 more
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On the stochastic porous medium equation
Journal of Differential Equations, 2006 The author proves existence and uniqueness for the Cauchy problem and the initial-boundary value problem \[ u_{t}=\sum_{i=1}^{n}\partial_{x_{i}}(| u| ^{p-2}\partial_{x_{i}}u)+\sum_{j=1}^{\infty}f_{j}{dB_{j}\over dt},\quad (t,x)\in (0,T)\times G, \] \(u=0\), \((t,x)\in (0,T)\times\partial G\), \(u(0,x)=u_0(x)\), \(x\in G\), where \(G\) is a bounded ...
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Boundary Regularity for the Porous Medium Equation [PDF]
Archive for Rational Mechanics and Analysis, 2018 We study the boundary regularity of solutions to the porous medium equation $u_t = u^m$ in the degenerate range $m>1$. In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the ...
Anders Björn +3 more
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Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media [PDF]
E3S Web of Conferences, 2022 The combined advection-diffusion-reaction (ADR) equation, which describe the transport problem of a contaminant in porous medium, does not generally admit an analytical solution.
El Arabi Inasse +2 more
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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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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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Acoustics of Fractal Porous Material and Fractional Calculus
Mathematics, 2021 In this paper, we present a fractal (self-similar) model of acoustic propagation in a porous material with a rigid structure. The fractal medium is modeled as a continuous medium of non-integer spatial dimension.
Zine El Abiddine Fellah +4 more
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From Darcy Equation to Darcy Paradox
Fluids, 2022 This theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach
Carmine Di Nucci, Daniele Celli
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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 u \geq 0 , u ∈ L loc m ( Ω ) u \in L_{{\text {loc}}}^m(\Omega ) , Ω ⊂ R
Dahlberg, Björn E. J., Kenig, Carlos E.
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