Results 21 to 30 of about 35,041 (167)
Porous Medium Equation with Nonlocal Pressure [PDF]
, 2018 We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (- )^{-s}u)$, which describes a flow through a porous medium driven by a nonlocal pressure. We consider constant parameters $m>1$ and $02$, and the asymptotic behavior of solutions when $N=1$. The cases $m = 1$
Stan, Diana +2 more
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Stochastic models associated to a Nonlocal Porous Medium Equation
Modern Stochastics: Theory and Applications, 2018 The nonlocal porous medium equation considered in this paper is a degenerate nonlinear evolution equation involving a space pseudo-differential operator of fractional order.
Alessandro De Gregorio
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The Toda Flow as a Porous Medium Equation
Communications in Mathematical Physics, 2023 We describe the geometry of the incompressible porous medium (IPM) equation: we prove that it is a gradient dynamical system on the group of area-preserving diffeomorphisms and has a special double-bracket form. Furthermore, we show its similarities and differences with the dispersionless Toda system.
Boris Khesin, Klas Modin
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Logarithmic corrections in Fisher–KPP type porous medium equations [PDF]
Journal de Mathématiques Pures et Appliquées, 2020 We consider the large time behaviour of solutions to the porous medium equation with a Fisher-KPP type reaction term and nonnegative, compactly supported initial function in $L^\infty(\mathbb{R}^N)\setminus\{0\}$: \begin{equation} \label{eq:abstract} \tag{$\star$}u_t= u^m+u-u^2\quad\text{in }Q:=\mathbb{R}^N\times\mathbb{R}_+,\qquad u(\cdot,0)=u_0\quad\
Du, Yihong +2 more
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Effect of soil consolidation on the fractality of the filtration law
International Journal of Applied Mechanics and Engineering, 2023 In this paper, the effect of consolidation of the soil structure on the fractality of the fluid flow was evaluated. The equation of fractal law of flow in the porous medium under consolidation of two-phase, fully fluid-saturated soil was determined ...
Geylani Panahov +2 more
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ROTARY VIBRATIONS OF A POROUS SPHERICAL SHELL WITH AN IMPERMEABLE CORE IN A VISCOUS LIQUID
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2020 Background. The investigation of the viscous liquid flows in contact with the oscillating submerged porous bodies of various configurations is of a considerable interest for hydrodynamics in the connection with a great theoretical importance and ...
O. A. Bazarkina, N. G. Taktarov
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On a fractional thin film equation
Advances in Nonlinear Analysis, 2020 This paper deals with a nonlinear degenerate parabolic equation of order α between 2 and 4 which is a kind of fractional version of the Thin Film Equation.
Segatti Antonio, Vázquez Juan Luis
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Revue des Énergies Renouvelables, 2022 The three-dimensional numerical simulation of laminar mixed convection heat transfer with and without porous medium in a cylindrical duct was carried out in this study. The cylinder is divided into three parts. The first and the third parts are adiabatic,
Amira Houichi +2 more
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A fractional porous medium equation
Advances in Mathematics, 2011 We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, $\frac{\partial u}{\partial t} + (- )^{1/2} (|u|^{m-1}u)=0$ in $\mathbb{R}^N$, with $m>m_*=(N-1)/N$, $N\ge1$ and $f\in L^1(\mathbb{R}^N)$.
de Pablo, Arturo +3 more
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Numerical Method for a Filtration Model Involving a Nonlinear Partial Integro-Differential Equation
Mathematics, 2022 In this paper, we propose an efficient numerical method for solving an initial boundary value problem for a coupled system of equations consisting of a nonlinear parabolic partial integro-differential equation and an elliptic equation with a nonlinear ...
Dossan Baigereyev +4 more
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