A Free Boundary Problem for ODE Arising from Degenerate Parabolic Equations

Assume B∈C0,+∞)∩)C~1(0,+∞) and B(υ) is strictly increasingand concave. That the free boundary Problem for ODE υ″=-1/2s〔B(υ)〕′for s>s_0, υ(s_0), υ′(s_0)=-(a/2)s_0, limυ(s)=βhas a unique solution (υ(s),s_0) with s_0∈〔-(2β/a)~(1/2),0) is proved. This problemarises, for example, from the investigation of the structure of discontinuous solutions for degenerate parabolic equations like(u/t)=A(u)/x~2