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Zbl 1120.34009
Brighi, Bernard; Hoernel, Jean-David
Similarity solutions for high frequency excitation of liquid metal in an antisymmetric magnetic field. (English)
[A] Biler, Piotr (ed.) et al., Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5--9, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 74, 41-57 (2006).

The authors consider the third order nonlinear autonomous differential equation $$f'''+\frac{m+1}{2}ff''-m{f'}^2=0$$ with the boundary conditions $$f(0)=a,\quad f'(0)=-1,\quad f'(\infty)=0,$$ where $m\in \Bbb R$ and $f'(\infty)=\lim_{t\to\infty}f'(t)$. Several existence results are established in both cases $m<0$ and $m>0$. The solutions of the above problem are similarity solutions of problems related to the phenomenon of high frequency excitation of liquid metal system in an antisymmetric magnetic field, within the framework of boundary layer approximation.
[Zaihong Wang (Beijing)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34C11 Qualitative theory of solutions of ODE: Growth, etc.
76D10 Boundary-layer theory (incompressible fluids)
34C60 Applications of qualitative theory of ODE

Keywords: third order differential equations; boundary value problems; plane dynamical systems; blowing up coordinates

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