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 \[ u_t=\Big(|(u^{m})_x|^{p-1}(u^{m})_x\Big)_x-bu^β, \, mp>1, \, β>0. \] 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.
math.AP↗