Analysis and Numerical Approximation of Singular Boundary Value Problems with the P-Laplacian in Fluid Mechanics

Journal of Computational and Applied Mathematics, 262 (2014), 87-104
http://dx.doi.org/10.1016/j.cam.2013.09.071

This paper studies a generalization of the Cahn–Hilliard continuum model for multi-phase fluids where the classical Laplacian has been replaced by a degenerate one (i.e., the socalled p-Laplacian). The solution’s asymptotic behavior is analyzed at two singular points; namely, at the origin and at infinity. An efficient technique for treating such singular boundary value problems is presented, and results of numerical integration are discussed and compared with earlier computed data.