Porous medium equation
Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms
... under homogeneous Dirichlet or Neumann boundary condition, and obtained the bounds for blow-up time of the solution to the initial boundary value problem in a three- dimensional space. Later, Liu [17] considered the ...
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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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Regularity of weak solutions of the Cauchy problem to a fractional porous medium equation
... This paper concerns the regularity of the weak solutions of the Cauchy problem to a fractional porous medium equation with a forcing term. In the recent work (Fan et al. in Comput. Math. Appl. ...
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Uniform blow-up rate for a porous medium equation with a weighted localized source
... 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 rate of ...
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Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition
... the porous medium equation, written here PME for ...Boussinesq's equation. The PME equation is one of the simplest examples of a nonlinear evolution equation of parabolic ...heat ...
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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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Numerical Simulation that Provides Non oscillatory Solutions for Porous Medium Equation and Error Approximation of Boussinesq's Equation
... In this paper, we focus our attention on degenerate parabolic equations such as the porous medium equation (PME). It is well known that the degeneracy implies a fi- nite speed of propagation [4, 6]. ...
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Extinction and decay estimates of solutions for a porous medium equation with nonlocal source and strong absorption
... In this paper, we investigate extinction properties of the solutions for the initial Dirichlet boundary value problem of a porous medium equation with nonlocal source and strong absorption terms. We ...
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Global existence and blow-up to the solutions of a singular porous medium equation with critical initial energy
... In this paper, we study a singular porous medium equation considered in [], where the global existence and blow-up conditions were got for the case of subcritical initial energy.. E ( u[r] ...
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Large time behavior of solutions for the porous medium equation with a nonlinear gradient source
... In this section, we establish the following comparison lemma between positive supersolu- tions and non-negative subsolutions to the elliptic equation in (.): which is an important tool for the uniqueness of the ...
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Complicated asymptotic behavior of solutions for a porous medium equation with nonlinear sources
... Suzuki, R: Asymptotic behavior of solutions of quasilinear parabolic equations with slowly decaying initial data.. Mukai, K, Mochizuki, K, Huang, Q: Large time behavior and life span for[r] ...
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Numerical methods to simulate moisture dynamics in fibrous sheet
... Comprehension of moisture dynamics in fibrous sheets is indispensable in a wide variety of industrial areas. This paper proposes a practical mathematical model, which is referred to as the 2-D extended porous ...
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NUMERICAL SOLUTION OF BERGERS’ EQUATION IN A ONE-DIMENSIONAL GROUNDWATER RECHARGE BY SPREADING USING FINITE DIFFERENCE METHOD
... differential equation as Burgers equation, with permeability as nonlinear function of moisture ...saturated porous media by using small parameter ...
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Stability of a spherical flame ball in a porous medium
... a porous solid, in which the solid serves only as a reservoir of heat and contributes nothing to conductive or radiative effects, the steady solutions themselves are exactly the same as they would be if no solid ...
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Heat transfer through porous medium: A Review
... through porous material has a great scope in chemical, mechanical, aerospace, medical, biological engineering, materials sciences & many more ...property, Porous material being a part of interest of ...
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Forced Convection In A Pipe Filled With Porous Medium
... with porous medium under constant heat flux condition. The porous in-serts used in this study is made of packed steel balls and the working fluid is ...with porous medium is explored ...
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Application of Green Function Method for Solution Advection Diffusion Equation of Nutrient Concentration in Groundwater
... where porosity of the water, is a Darcy flux of pore water, is a diffusion coefficient of nutrients in pore water, is the interfacial ion transport, which is non-zero if the liquid is below saturation. Now let Darcy flux ...
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Reaction infiltration instability in a compacting porous medium
... where ζ is an effective compaction or bulk viscosity. The solid matrix behaves like a rigid porous matrix when the bulk viscosity is sufficiently large (an idea we will relate to a non-dimensional matrix stiffness ...
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Heat Transfer Characteristics of Porous Radiant Burners Using Discrete-Ordinate Method (S2-Approximation)
... energy equation is obtained using central differencing for derivative terms where the error of discretization is the order of ( ∆ X ) 2 ...Energy equation for solid phase is an algebraic one and the ...
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Critical extinction exponents for a fast diffusion equation with nonlocal source and absorption
... Proof of Theorem . (i) Let u(x, t) be any solution of (.). It can be verified that, for the case m = q < r < , a sufficiently large constant L is a super-solution of (.). Therefore, we know that u(x, t) ≤ L in ...
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