Similarity solutions for liquid metal systems near a sharply cornered conductive region
The following boundary value problem \[ \begin{cases} f''' + [(m+1)/2]ff'' - m {f'}^2 = 0 \quad \text{on}\;(0,+\infty), \\ f(0)=a \in {\mathbb R}, \quad f'(0)=-1, \quad f'(+\infty) = 0 \end{cases} \] is considered. The problem arises in the study of similarity solutions for high frequency excitation of liquid metal systems in an antisymmetric magnetic field. A complete picture of solutions is given for the physical interesting case when \(m<-1\) and \(a\geq 0\).
scientific article; zbMATH DE number 5555257
scientific article