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arXiv · 1709.06676

Evolution of Interfaces for the Nonlinear Double Degenerate Parabolic Equation of Turbulent Filtration with Absorption

Ugur G. Abdulla·Jian Du·Adam Prinkey·Chloe Ondracek·Suneil Parimoo
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Abstract

We prove the short-time asymptotic formula for the interfaces and local solutions near the interfaces for the nonlinear double degenerate reaction-diffusion equation of turbulent filtration with strong absorption \[ u_t=\Big(|(u^{m})_x|^{p-1}(u^{m})_x\Big)_x-bu^β, \, mp>1, \, β>0. \] Full classification is pursued in terms of the nonlinearity parameters $m, p,β$ and asymptotics of the initial function near its support. Numerical analysis using a weighted essentially nonoscillatory (WENO) scheme with interface capturing is implemented, and comparison of numerical and analytical results is presented.

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Ugur G. Abdulla, Jian Du, Adam Prinkey, Chloe Ondracek, Suneil Parimoo. 2017-09-19. Evolution of Interfaces for the Nonlinear Double Degenerate Parabolic Equation of Turbulent Filtration with Absorption. https://doi.org/10.1016/j.matcom.2018.05.017

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