Results 31 to 40 of about 35,041 (167)
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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The porous medium equation in one dimension [PDF]
Transactions of the American Mathematical Society, 1977 We consider a second order nonlinear degenerate parabolic partial differential equation known as the porous medium equation, restricting our attention to the case of one space variable and to the Cauchy problem where the initial data are nonnegative and have compact support consisting of a bounded interval.
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Concavity of Solutions of the Porous Medium Equation [PDF]
Transactions of the American Mathematical Society, 1987 We consider the problem \[ ( P ) { u t =
Benilan, Philippe, Vazquez, Juan Luis
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Blow up for Porous Medium Equations
Mathematical Sciences and Applications E-Notes, 2021 In various branches of applied sciences, porous medium equations exist where this basic model occurs in a natural fashion. It has been used to model fluid flow, chemical reactions, diffusion or heat transfer, population dynamics, etc.. Nonlinear diffusion equations involving the porous medium equations have also been extensively studied. However, there
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Microscopic Dynamics for the Porous Medium Equation [PDF]
, 2011 In this work, I present an interacting particle system whose dynamics conserves the total number of particles but with gradient transition rates that vanish for some configurations. As a consequence, the invariant pieces of the system, namely, the hyperplanes with a fixed number of particles can be decomposed into an irreducible set of configurations ...
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Applications of Computational Modelling and Simulation of Porous Medium in Tissue Engineering
Computation, 2016 In tissue engineering, porous biodegradable scaffolds are used as templates for regenerating required tissues. With the advances in computational tools, many modeling approaches have been considered.
Carrie L. German +1 more
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An X–FEM technique for numerical simulation of variable-density flow in fractured porous media
MethodsX, 2023 Solute transport is one of the major topics in geological studies. Fracture is a significant characteristic of natural porous media, where the solute can transport due to its higher density with respect to the density of fluid.
A.R. Khoei +3 more
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Perron's method for the porous medium equation [PDF]
Journal of the European Mathematical Society, 2016 This work extends Perron’s method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in a general cylindrical domain.
Lukkari, Teemu +3 more
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Unsteady Oscillatory Flow and Heat Transfer in a Horizontal Composite Porous Medium Channel
Nonlinear Analysis, 2009 The problem of unsteady oscillatory flow and heat transfer in a horizontal composite porous medium is performed. The flow is modeled using the Darcy-Brinkman equation.
J. C. Umavathi +3 more
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Solutions of a Class of Degenerate Kinetic Equations Using Steepest Descent in Wasserstein Space
Journal of Mathematics, 2020 We use the steepest descent method in an Orlicz–Wasserstein space to study the existence of solutions for a very broad class of kinetic equations, which include the Boltzmann equation, the Vlasov–Poisson equation, the porous medium equation, and the ...
Aboubacar Marcos, Ambroise Soglo
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