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Interaction of Droplet Diffusions Governed by 2-D Porous Medium Equation

Edi Cahyono, La Hamimu, La Ode Ngkoimani and Jamhir Safani
This paper considers two dimensional (2D) porous medium equation (PME). PME yields a solution, the so-called Barenblatt’s solution (BS). For the limiting case, it is the fundamental solution of the heat equation. An interpretation of the application of BS is the diffusion of a droplet of ink on a piece of paper. This paper discusses the interaction of the diffusion of two droplets governed by PME. While the analytical solution is still hard to obtain, the solution sought numerically by applying a finite difference method. The numerical solution does not show the presence of ‘nipple’ like figure before, during and after the collision of the droplets as the superposition of droplets does. This confirms and generalizes the previous results on one dimensional PME. Mathematical Subject Classification: 35K05, 35K50, 35A08, 65M06 Keywords: Porous medium equation, Heat equation, Barenblatt’s solution

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Diterbitkan pada: Applied Mathematical Sciences Vol. 8, No. 127, Th 2014 ISSN 1312-885X (print) ISSN 1314-7552 (online)

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