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

Kulikov, Gennady Yu; Lima, Pedro M.; Morgado, M. Luísa

Journal of Computational and Applied Mathematics, 262 (2014), 87-104

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studies a generalization of the Cahn–Hilliard continuum model for multi-phase fluids where the classical Laplacian has been replaced by a degenerate one (i.e., the socalled p-Laplacian).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.