Evolution of interfaces for the nonlinear double degenerate parabolic equation of turbulent filtration with absorption

Ugur G. Abdulla, Jian Du, Adam Prinkey, Chloe Ondracek and Suneil Parimoo

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 153, issue C, 59-82

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 ut=(|(um)x|p−1(um)x)x−buβ,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.

Keywords: Nonlinear degenerate parabolic PDE; Reaction–diffusion equation; Interface; Nonlinear scaling laws; Super- and subsolutions (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:153:y:2018:i:c:p:59-82

DOI: 10.1016/j.matcom.2018.05.017

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