Existence and Uniqueness of Very Singular Solution of a Degenerate Parabolic Equation with Nonlinear Convection. (5th May 2009) - Fang, Zhong Bo; Piao, Daxiong; Wang, Jian
Abstract : We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation:( | f ′ | p − 2 f ′ ) ′ + β r f ′ + α f + ( f q ) ′ = 0 satisfying a specific decay rate:lim   r → ∞ r α / β f ( r ) = 0 withα : = ( p − 1 ) / ( p q − 2 p + 2 ) andβ : = ( q − p + 1 ) / ( p q − 2 p + 2 ) . Herep > 2 andq > p − 1 . Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection termu t = ( | u x | p − 2 u x ) x + ( u q ) x defined on the half line[ 0, + ∞ ) .