Mar 25, 2017 · For the spherical symmetric case the energy is being spread out across the surface of a 3D-sphere which has surface area 4πr2. The factors of r2 ...
Two theorems are proved for the spherically symmetric solutions of the “bistable” reaction-diffusion equation ƒ u t = Δ x u + ƒ(u) , where ƒ is cubic-like ...
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We introduce a general and versatile MS Windows application for solving the spherically symmetric diffusion problem, involving up to two coupled spherically ...
Introduction. The present paper extends some earlier work [1] on heat flow in a composite system, in which a central, high-temperature region loses heat.
Oct 23, 2018 · For steady state diffusion in an unbounded region toward a spherical sink of radius r0, we have 4πr2Ddcdr=Q. where Q is the diffusion rate ...
Jan 31, 2024 · We resolve a long-standing question regarding the suitable effective diffusion coefficient of the spherical-symmetric transport equation, ...
We prove two theorems here. The first is a complete description of the possibilities for spherically symmetric initial data that are nonincreasing in the radial ...
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The spherically symmetric diffusion problem (SSDP) has a wide variety of applications, depending on dimensionality, boundary condi- tions, initial distribution, ...
May 3, 2022 · 3.5.3 Diffusion within a sphere. As an application of spherical coordinates, let us consider the diffusion of a scalar density.