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

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.