The porous medium equation
CiteSeerX — Microscopic dynamics for the porous medium equation
... equation Patr´ıcia Gonc¸alves Abstract In this work, I present an interacting particle system whose dynamics conserves the total number of particles but with gradient transition rates that van- ish for some ...
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COMPLICATED LARGE TIME BEHAVIOR IN POROUS MEDIUM EQUATION WITH ABSORPTIONS
... Remark 1. If 𝑝−𝑚 2 < 𝜎 < 𝑁, the complexity may occur in the large time behavior of the solutions for the problem (1.1)–(1.2), see details in [7]. But for 𝜎 = 𝑝−𝑚 2 , we cannot get this result for the problem ...
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Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition
... un-natured porous medium equation, the convective part may re- present the effect of ...Boussinesq equation of hydrology, which is involved in various fields of petroleum technology and ground ...
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Asymptotic behaviour of solutions for porous medium equation with periodic absorption
... with porous medium equation with periodic absorp- ...the equation. In contrast to the equation without sources, we show that the solutions may not decay but may be “attracted” into any ...
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Well posedness of a fractional porous medium equation on an evolving surface
... In order to facilitate all of this, we begin by studying (in the setting of closed Riemannian manifolds and Sobolev spaces) the fractional Laplace–Beltrami operator which can be seen as the Dirichlet-to-Neumann map of a ...
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Complicated asymptotic behavior of solutions for a porous medium equation with nonlinear sources
... 15. Kamin, S, Peletier, LA: Large time behaviour of solutions of the heat equation with absorption. Ann. Sc. Norm. Super. Pisa, Cl. Sci. 12(3), 393-408 (1985) 16. Bénilan, P, Crandall, MG, Pierre, M: Solutions of ...
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Regularity of weak solutions of the Cauchy problem to a fractional porous medium equation
... Full list of author information is available at the end of the article Abstract This paper concerns the regularity of the weak solutions of the Cauchy problem to a fractional porous medium equation ...
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The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions
... The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions Piotr Biler, Cyril Imbert & Grzegorz Karch Communicated by L.. Abstract A degenerate nonlinear nonlocal [r] ...
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Uniform blow-up rate for a porous medium equation with a weighted localized source
... Abstract In this article, we investigate the Dirichlet problem for a porous medium equation with a more complicated source term. In some cases, we prove that the solutions have global blow-up and the ...
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Extinction and decay estimates of solutions for a porous medium equation with nonlocal source and strong absorption
... Full list of author information is available at the end of the article Abstract In this paper, we investigate extinction properties of the solutions for the initial Dirichlet boundary value problem of a porous ...
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Global existence and blow-up to the solutions of a singular porous medium equation with critical initial energy
... Abstract This paper is devoted to the study of a singular porous medium equation, which was studied extensively in recent years. We obtain the global existence and blow-up condition at the critical ...
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Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
... the porous medium equation in an exterior two- dimensional domain that excludes a hole, with zero Dirichlet data on its bound- ...the equation with a variable mass that decays to 0 in a ...
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Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms
... Full list of author information is available at the end of the article Abstract We investigate the blow-up phenomena for a porous medium equation with weighted nonlocal source and inner absorption ...
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Numerical Simulation that Provides Non oscillatory Solutions for Porous Medium Equation and Error Approximation of Boussinesq's Equation
... In order to study numerically any kind of problem we need a stable and consistent numerical scheme [7, 11, 9]. Besides, a good scheme has to reproduce all of the important features of the original model, which arise from ...
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Large time behavior of solutions for the porous medium equation with a nonlinear gradient source
... Am. Math. Soc. (N.S.) 27, 1-67 (1992) 7. Arrieta, JM, Bernal, AR, Souplet, P: Boundedness of global solutions for nonlinear parabolic equations involving gradient blow-up phenomena. Ann. Sc. Norm. Super. Pisa, Cl. Sci. ...
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Key words Kinetic equation, Macroscopic limit, Diffusion limit, Boltzmann equation, Equilibrium dis- tribution function, Gibbs state, Porous medium equation, Fast diffusion equation, Relaxation time ap- proximation, Compensated compactness
... Nonlinear diffusion equations have attracted a lot of attention over the last few years, because of their deep mathematical properties and the physical interpretation of their naturally associated Lyapunov functionals. A ...
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Mechanisms of dispersion in a porous medium
... The distribution of mean pore velocities is much narrower than the distribution of the Eulerian velocity magnitude, with smooth cut-offs at low and high velocity magnitudes. Then, we cast the advective-diffusive ...
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The effect of a fissure on storage in a porous medium
... evolution equation describing the sharp interface between buoyant and ambient reservoir ...evolution equation generally admits similarity solutions which are a powerful tool with which to quickly assess the ...
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The Rayleigh Taylor instability in a porous medium
... in porous media, perhaps in situations where leaching fluid is pumped into an ore-bearing rock, in an attempt to dis- solve and extract the ore ...the porous medium, the gradient of the fluid pore ...
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A PHENOMENOLOGICAL MODEL OF SUSPENSION FILTRATION IN POROUS MEDIUM
... in porous media many phenomenologi- cal relationships have been obtained, but “aging” and “charging” phenomena not taken account ...a porous medium with tacking into account all stages of filtration ...
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