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Periodic solutions for a porous medium equation
Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this paper, we study with a periodic porous medium equation with nonlinear convection terms and weakly nonlinear sources under Dirichlet boundary conditions.
Dazhi Zhang, Jiebao Sun, Boying Wu
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System of porous medium equations [PDF]
Journal of Differential Equations, 2021 We investigate the evolution of population density vector, $\bold{u}=\left(u^1,\cdots,u^k\right)$, of $k$-species whose diffusion is controlled by its absolute value $\left|\bold{u}\right|$. More precisely we study the properties and asymptotic large time behaviour of solution $\bold{u}=\left(u^1,\cdots,u^k\right)$ of degenerate parabolic system \begin{
Kim, Sunghoon, Lee, Ki-Ahm
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The mathematical model of gas flowing in porous medium based on the homogenization method [PDF]
E3S Web of Conferences, 2021 Considered the characteristics of porous medium in the coal seam and goaf, in order to reflect the accurately influence of various porous media against the gas flow, the mathematical model of discrete multi-scale network and macroscopic flow, CFCM (Coal ...
Xiong Wei
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The Thermal Performance Analysis of an Al2O3-Water Nanofluid Flow in a Composite Microchannel
Nanomaterials, 2022 Partial filling of porous medium insert in a channel alleviates the tremendous pressure drop associated with a porous medium saturated channel, and enhances heat transfer at an optimum fraction of porous medium filling.
Mirza Farrukh Baig +2 more
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Boundary Value Problems, 2023 In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main objectives of studying the fractional porous medium equation in the corresponding critical function spaces ...
Muhammad Zainul Abidin, Muhammad Marwan
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Numerical study of the process of unsteady flow in a three-layer porous medium
Magazine of Civil Engineering, 2023 The unsteady fluid flow in a three-layer porous medium is numerically investigated and is an important and topical problem. An analytical solution of the equation for the pressure fluid layer is obtained on the basis of the theory of elastic regime ...
Ravshanov Normahmad +3 more
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Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media
Entropy, 2021 A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines.
Dick Bedeaux, Signe Kjelstrup
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Mathematics, 2021 In this paper, we consider the generalized porous medium equation. For small initial data u0 belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using ...
Muhammad Zainul Abidin, Jiecheng Chen
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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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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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