A free boundary problem involving convection and singular absorption (Q1974222)

The principal objective in this paper is to study the existence of free boundary solutions to the problem \[ y''-\lambda(y^q)'-a(x)y^p=0,\quad y\geq 0\;\text{ in } (0,\infty), \qquad y(0)=\gamma,\quad y'(0)=0, \] with \[ \gamma>0,\quad q\geq 0,\quad 0<p<1,\quad \lambda\in \mathbb{R}. \] This problem arises when investigating stationary free boundary solutions to a parabolic equation with convection and singular absorption. Existence and qualitative properties of free boundary solutions are established.